100 Question 100 Min. Series Electrostatics

A NAME IN CONCEPTS OF PHYSICS

XI &XII (CBSE & ICSE BOARD)

IIT-JEE / NEET /AIIMS / JIPMER / uptU

A charged ball B hangs from a silk thread S, which makes an angle  with a large charged conducting sheet P, as shown in the figure. The surface charge density  of the sheet is proportional toOn moving a charge of 20 C by 2 cm, 2 J of work is done, then the potential difference between the points is(1) 0.1 V

(2) 8 V

(3) 2 V

D

H

C O • q

(1) q/40L

(2) zero

(3) q/20L

(4) q/30L

A thin spherical conducting shell of radius R has a charge q. Another charge Q is placed at the centre of the shell. The electrostatic potential at a point P at a distance R/2 from the centre of the shell is2Q 2Q 2q – (1) (2) 4  0 R 4  0 R 4 0 R 4  0 R

q 4  0 R

(4)

( q  Q) 2

L

(3) r/2

•

r

Q •

(4) r/4

Four charges equal to –Q are placed at the four corners of a square and a charge q is at its centre. If the system is in equilibrium, the value of q isQ Q (1)– (1 + 2 2 ) (2) (1 + 2 2 ) 4 4 Q Q (3) – (1 + 2 2 ) (4) (1 + 2 2 ) 2 2

(3) 8L

4

(4) 4L

Two thin wire rings each having a radius R are placed at a distance d apart with their axes coinciding. The charges on the two rings are +q and –q. The potential difference between the centres of the two rings is-

(1)

qR 4  0 d

2

4 0 R

q v • • • • • • • •

(2) 2r

(2)

(3) zero

Two spherical conductors B and C having equal radii and carrying equal charges in them, repel each other with a force F when kept apart at some distance. A third spherical conductor having same radius as that of B but uncharged, is brought in contact with B, then brought in contact with C and finally removed away from both. The new force of repulsion between B and C is3F 3F F F (1) (2) (3) (4) 4 8 4 8 A charged particle q is shot towards another charged particle Q which is fixed, with a speed v. It approaches Q upto a closest distance r and then returns. If q was given a speed 2v, the closest distance of approach would be-

(1) r

(1) cos (2) cot (3) sin (4) tan – Two point charges + 8q and 2q are located at x = 0 and x = L respectively. The location of a point on the x-axis at which the net electric field due to these two point charges is zero is(1) 2L

B L

+

•B

A

G

2Q

S

q •

F

(3)



(4) 0.5 V

A charged particle q is placed at the centre O of cube of length L (ABCDEFGH). Another same charge q is placed at a distance L from O. Then the electric flux through ABCD isE

P

1 1    2 2  2 0 R R  d   1 q 1   (4)   4  0 R R2  d2  

(2)

q

An electric dipole is placed at an angle of 30 to a nonuniform electric field. The dipole will experience(1) a translational force only in the direction of the field (2) a translational force only in a direction normal to the direction of the field (3) a torque as well as a translational force (4) a torque only Two spherical conductors A and B of radii 1 mm and 2 mm are separated by a distance of 5 cm and are uniformly charged. If the spheres are connected by a conducting wire then in equilibrium condition, the ratio of the magnitude of the electric fields at the surfaces of spheres A and B is(1) 4: 1 (2) 1: 2 (3) 2: 1 (4) 1: 4 An electric charge 10–3 µC is placed at the origin (0, 0) of X-Y coordinate system. Two points A and B are situated at ( 2 , 2 ) and (2, 0) respectively. The potential difference between the points A and B will be(1) 9 V

(2) zero

(3) 2V

(4) 4.5 V

ELECTROSTATICS FORCE & FIELD

P.L . SHARMA ROAD, ROAD, center SHASTRI NAGAR NAGAR center CENTRAL MARKET, Opp. Sagar Complex Meerut

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Charges are placed on the vertices of a square as shown.  Let E be the electric field and V the potential at the centre. If the charges on A and B are interchanged with those on D and C respectively, thenq

q

A

B

D

C

–q

–q

 (1) E Remains unchanged, V changes  (2) Both E and V change  (3) E And V remain unchanged  (4) E Changes and V remains unchanged The potential at a point x (measured in µm) due to to some charges situated on the x-axis is given by: V(x) = 20/(x2 – 4) volt. The electric field E at x = 4 µm is given by 5 (1) V/µm and in the –ve x direction 3 5 (2) V/µm and in the +ve x direction 3 10 (3) V/µm and in the –ve x direction 9 10 (4) V/µm and in the +ve x direction 9 A thin spherical shell of radius R has a charge Q spread uniformly over its surface. Which of the following graphs most closely represents the electric field E(r) produced by the shell in the range 0  r   , where r is the distance from the centre of the shell? E(r)

E(r)

(1)

(3)

O E(r)

O

R

r

(2) O

r

R

This question contains Statement– 1 and Statement– 2. 2. Of the four choices given after the statements, choose the one that best describes the two statements. Statement– 1: 1: For a charged particle moving from point P to point Q the net work done by an electrostatic field on the particle is independent of the path connecting point P to point Q. Statement– 2: 2: The net work done by a conservative force on an object moving along closed loop is zero (1) Statement–1 is true, Statement–2 is true; Statement–2 is not the correct explanation of Statement –1 (2) Statement–1 is false, Statement–2 is true (3) Statement–1 is true, Statement–2 is false (4)Statement–1 is true, Statement–2 is true; Statement –2 is the correct explanation of Statement –1 Two points P and Q are maintained at the potential of 10V and –4V, respectively. The work done in moving 100 electrons from P to Q is :(1) –2.24 × 10 –16 J (3) –9.60 × 10 –17 J Let (r) =

r

(4)

O

R

r

A charge Q is placed at each of the opposite corners of a square. A charge q is placed at each of the other two Q corners. If the net electrical force on Q is zero, then q equals: 1 (1) 1 (2)  (3) 2 2 (4) –1 2

R 4

r be the charge density distribution for a

solid sphere of radius R and total charge Q. For a point 'p' inside the sphere at distance r 1 from the centre of the sphere, the magnitude of electric field is 2

(1)

2

Qr1

4  0 R

4

(3) 0

(2) (4)

Qr1

3  0 R

4

Q 4  0 r1

2

A thin semi-circular ring of radius r has a positive charge q distributed uniformly over it. The net field E centre O is q q ˆ ˆ (1) (2) j j 2 2 2 2  0 r 4  0 r 2 (3)

E(r)

R

Q

(2) 2.24 × 10–16 J (4) 9.60 × 10–17 J



q 4

2

0 r

2

ˆ j

(4)



q 2

2

0 r 2

at the

ˆ j

Let there be a spherically symmetric charge distribution with charge density varying as 5 r  (r) = 0    up to r = R, and (r) = 0 for r > R, 4 R where r is the distance from the origin. The electric field at a distance r (r < R) from the origin is given by : (1) (3)

0 r  5 r     30  4 R  0 r  5 r     40  3 R 

(2) (4)

40 r  5

r    3 0  3 R  4 0 r  5 r     3 0  4 R 







Two identical charged spheres are suspended by strings of equal lengths. The strings strings make an angle of 30 with each other. When suspended in a liquid of density 0.8 g cm –3, the angle remains the same. If density of the material of the sphere is 1.6 g cm –3, the dielectric constant of the liquid is : (1) 1 (2) 4 (3) 3 (4) 2

(1) Statement-1 is true, Statement-2 is true and Statement-2 is the correct explanation of Statement-1. (2) Statement-1 is true, Statement-2 is true and Statement-2 is not the correct explanation of statement-1. (3) Statement-1 is true, Statement-2 is false (4) Statement-1 is false, Statement-2 is true.

Two identical charged spheres suspended from a common

In a uniformly charged sphere of of total total charge Q and radius R, the electric field E is plotted as a function of distance from the centre. The graph which would correspond to the above will be :-

point by two massless string of length  are initially a distance d(d << ) apart because of their mutual repulsion. The charge begins to leak from both the spheres at a constant rate. As a result the charges approach each other with a velocity v. Then as a function of distance x between them :(1) v  x1/2

(2) v  x

(3) v  x–1/2

(4) v  x–1

(1) –24 a0

(2) –6 a0

(3) –24 a0r

(4) – 6 a0r

4 0

a

1  

  5

1

(4)

1 4  0

(3)

2qQ  a

1  

E

R

(4)

r

R

r



q 2

is placed at the origin. If charge q 0 is given a small displacement (y << a) along the y-axis, the net force acting on the particle is proportional to (1) y

(2) –y

1

(3)

y

(4) –

1 y

A charge Q is uniformly distributed over a long rod AB of length L as shown in the figure. The electric potential at the point O lying at a distance L from the end A is :-

  5

q 3 0 The electric field at a distance r (r < R) from

r 3 0

r

2

An insulating solid sphere of radius R has a uniformly positive charge density . As a result of this uniform charge distribution there is a finite value of electric potential at the centre of the sphere, at the surface of the sphere and also at a point outside the sphere. The electric potential at infinity is zero. When a charge 'q' is taken from the centre to the surface of the sphere, its potential energy changes

the centre of the sphere is

R

Two charges, each equal to q, are kept at x = –a and x =

(1)

by

(2)

r

a on the x-axis. A particle of mass m and charge q 0

Two positive charges of magnitude 'q' are placed at the ends of a side (side 1) of a square of side '2a'. Two negative charges of the same magnitude are kept at the other corners. Starting from rest, if a charge Q moves from the middle of side 1 to the centre of square, its kinetic energy at the centre of square is :1 2qQ  1  1 (1) (2) zero   4 0 a  5 2qQ 

R E

is given by  = ar2 + b where r is the distance from the centre; a, b are constant. Then the charge density inside the ball is :-

1

E

(1)

The electrostatic potential inside a charged spherical ball

(3)

E

(3)

Q 8 0 L

Q 4 0 L ln 2

(2)

(4)

3Q 4 0 L Qln2 4 0 L

A charge +q +q is fixed at each of the points x = x0, x = 3x 0, x = 5x0........ on the x –axis and a charge –q is fixed at each of the points x = 2x0, x = 4x 0, x = 6x 0....... Here x0 is a positive constant. Take the electric potential at a point due to a charge Q at a distance r from it to be Q/4 0r. Then the potential at the origin to the above system of charges is :– q (A) Zero (B) 80 x0 n 2

. (C) Infinite

(D)

q n(2) 40 x 0







Three charges Q, +q and +q are are placed placed at the vertices of a right angle triangle (isosceles triangle) as shown. The net electrostatic energy of the configuration is zero, if Q is equal to :

of the following arrangements of charge is possible for, P, Q, R, S, T and U respectively respectively ? P

Q

Q O

U

T

+q

(A)

q 1 2

(B)

+

a

2q 2 2

(C) –2q

(D) +q

Three positive charges of equal value q are placed at the vertices of an equilateral triangle. The resulting line of force should be sketched as in

(A) +, –, +, –, –, + (C) +, +, –, +, –, –

R

S

(B) +, –, +, –, +, – (D) –, +, +, –, +, –

Consider the charge configuration and and a spherical Gaussian surface as shown in the figure. When calculating the flux of the electric field over the spherical surface, the electric field will be due to : q2

+q1

(A)

 q1

(B) (A) q2 (C) all the charges

(C) (D) A uniform electric field pointing in positive x–direction exists in a region. Let A be the origin, B be the point on the x–axis at x = +1 cm and C be on the point on the y – axis at y = +1cm. Then the potentials at the A, B and C satisfy : (A) VA < VB (B) VA > VB (C) VA < VC (D) VA > VC

(B) only the positive charges (D) +q1 and –q1

Three infinitely infinitely long charge sheets sheets are placed which charge density as shown in figure. The electric field at point P is :– z

z = 3a

 P

Two equal point charges are fixed at x = –a and x = +a on the x–axis. Another point charge Q is placed at the origin. The change in the electrical potential energy of Q, when it is displaced by a small distance x along the x –axis, is approximately proportional to : (A) x (B) x2 (C) x3 (D) 1/x A metallic shell has a point charge q kept inside its its cavity. Which one of the following diagrams correctly represents the electric lines of forces ?

(A)

(B)

(C)

(D)

Six charges, three positive and three negative negative of equal magnitude are to be placed starts from P in clockwise order at the vertices of a regular hexagon such that the electric field at O is double the electric field when only one positive charge of same magnitude is placed at R. Which

(A)

 

z= 0 x

– 

z = –a

2 ˆ k

0

(B)



2 ˆ k

0

(C)

4 ˆ k

0

(D)



4 ˆ k

0

A long, hollow conducting cylinder is kept coaxialy inside another long, hollow conducting cylinder of larger radius. Both the cylinders are initially electrically neutral : – (A) A potential difference appears between the two cylinders when a charge density is given to the inner cylinder (B) A potential difference appears between the two cylinders when a charge density is given to the outer cylinder (C) No potential difference appears between the two cylinders when a uniform line charge is kept along the axis of the cylinder (D) No potential difference appears between the two cylinders when same charge density is given to both the cylinder







Consider a neutral conducting sphere. A positive point charge is placed outside the sphere. The net charge on the sphere is then (A) Negative and distributed uniformly over the surface of the sphere (B) Negative and appears only at the point on the sphere closest to the point charge (C) Negative and distributed non–uniformly over the entire surface of the sphere

A disk of radius a/4 having a uniformly distributed charge 6 C is placed in the x-y plane with its centre at (– a/2, 0, 0). A rod of length a carrying a uniformly distributed charge 8 C is placed on the x-axis from x = a/4 to x = 5a/4. Two point charges – 7 C and 3 C are placed at (a/4,– a/4, 0) and (– 3a/4, 3a/4, 0), respectively. Consider a cubical surface formed by six surfaces x = ± a/2, y = ± a/2, z = ± a/2. The electric flux through this cubical surface is :-

y

(D) Zero. A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as shown in the figure. The electric field inside the emptied space is

x

(A)

(A) Zero everywhere (C) non–uniform .

Positive and negative point charges of equal magnitude a a    are kept at  0,0,  and  0,0,  respectively. The 2 2    work done by the electric field when another positive point charge is moved from (–a, 0, 0) to (0, a, 0) is

(A) 1: 2: 3

(C) Zero

.

y B C O

x

2C

0

(C)

10C

0

(D)

12C

0

(B) 1: 3: 5

(C) 1: 4: 9

(D) 1: 8: 18

Under the influence of the Coulomb field of charge +Q, a charge – q is moving around it in an elliptical orbit. Find out the correct statement(s) :(A) The angular momentum of the charge –q is constant

(B) negative

(D) Depends on the path connecting the initial and final positions q q 2q , and  Consider a system of three charges 3 3 3 placed at points points A, B and C, respectively, respectively, as shown shown in the figure. Take O to be the centre of the circle of radius R and angle CAB = 60 .

(B)

Three concentric metallic spherical shells of radii R, R, 2R, 3R, are given charges Q1, Q 2, Q 3, respectively. It is found that the surface charges densities on the outer surfaces of the shells are equal. Then, the ratio of the charges given to the shells, Q1: Q2: Q3, is

(B) Non–zero and uniform (D) zero only at its centre

(A) Positive

2C 0

(B) The linear momentum of the charge –q is constant (C) The angular velocity of the charge – q is constant (D) The linear speed of the charge – q is constant .

An elliptical cavity is carved within a perfect conductor. A positive charge q is placed at the centre of the cavity. The points A and B are on the cavity surface as shown in the figure. Then: A

60 A

q

(A) The electric field at point O is

q 8  R 2

B

directed

0

along the negative x–axis

(A) Electric field near A in the cavity = electric field near B

(B) The potential energy of the system is zero (C) The magnitude of the force between the charges at C and B is

q2 540 R

(B) Charge density at A = char ge density at B (C) Potential at A = potential at B

2

(D) The potential at point O is

in the cavity

(D) Total electric field flux through the surface of the cavity

q 12 R

is q/0

0







A solid metallic sphere has a charge + 3Q. Concentric with this sphere is a conducting spherical shell having charge –Q. The radius of the sphere is 'a' and that of the spherical shell is 'b' (b > a). What is the electric field at a distance R (a < R < b) from the centre 4Q 3Q (1) (2) 2 2 2 0 R 4 0 R (3)

3Q 2 0 R

2

6q

q 3q

q

0

 2 0

a

q

q

a

a q

q a

B

(1)



kq a

kq

2

C

(2)

2q

3kq

(2) III

(3) I

(4) II

Three charges Q, +q and +q are placed at the vertices of a right-angle isosceles triangle as shown in figure. The net electrostatic energy of the configuration is zero. Q is equal to

Q

+q

a

q 1 2

(2)

(3) –2q

2q 2 2

a

4  0 1 4  0

2q

. a .

2

(2) zero

 b2 q

(4)

1

.

q

4  0 a 2  b2 a 2  b2 A hollow metal sphere of radius 5 cm is charged such that the potential on its surface is 10 volts. The electric field at the centre of the sphere will be

(1) 50 volt / meter

(2) 10 volt / meter

(3) 5 volt / meter

(4) zero

(1) The path of the electron will be a circle

Electric field at the centre 'O' of of a semicircle of radius 'a' having linear charge density  is given as



(3)

1

–q

An electron enters an electric field with its velocity in the direction of the electric lines of field then : –

(4) +q

O

2

C

+q

q

(1)

(1)

2a2

A

IV

+q

2

q

III

(1) IV

kq

2q

q

2q



2

B 2q

a

(4) 2 2 2a a As shown in the fig. charges + q and – q are placed at the vertices B and C of an isosceles triangle. The potential at the vertex A is

q

2q

q

  0

(4)

II

2q

a

In the fig. force force on charge at A in the direction normal to BC will be :–

(3)

q

I

2q



a

0

(3)



(2)

q A

–q

–q

2q



20 R

Two positive point charge of 12 C and 8 C are 10 cm apart. The work done in bringing them 4 cm closer is, (1) 1.3 Ev (2) 13 J (3) 5.8 J (4) 5.8 eV Figure below show regular hexagon, the charges are placed at the vertices. In which of the following cases the electric field at the centre is zero. 4q

2

Q

(4)

5q

(1)

(2) The path of the electron will be a parabola (3) Velocity of the electron will decrease just after enter (4) Velocity of the electron will increase just after enter A cube of of metal metal is given a charge charge (+ Q), which which of of the following statements is true (1) potential at the surface of cube is zero (2) potential within the cube is zero (3) electric field is normal to the surface of the cube (4) electric field varies within the cube







Electric charge is uniformly distributed along a long straight wire of radius 1 mm. The charge per cm. length of the wire wire is Q coulomb. Another cylindrical surface of radius 50 cm. and length 1 m. symmetrically encloses the wire as shown in fig. The total flux passing through the cylindrical surface is :–

0

(2)

100Q

(3)

0

(2) r–1, r–2

(4) zero

Two point charges placed at a distance 'r' in air exert a force 'F'. The value of distance at which they exerts same force when placed in medium (dielectric constant K) is : – (2) r/K

(3) r

K

(4) r K

(1) Execute S.H.M. about the origin. 10 Q

 0

(4)

100Q

 0

The electric potential and field at a point due to an electric dipole are proportional to (1) r, r–1

(3) 120 V/m

Two equal negative charges – q, are placed at points (0,a) and (0,–a) on y axis, one positive charge q at rest is left to move from point (2a, 0). This charge charge will be

50cm Q

(1) 100 V/m (2) 125 V/m

(1) r K

1m

(1)

The electric field, at a distance of 20 cm from the centre of a dielectric sphere of radius 10 cm is, 100 V/m. Then E at 3 cm distance from the centre of sphere is

(3) r–2, r–3

(4) r–2, r–2

If in a region V = 4x2 volt then electric field at 2) m. is –

(1, 0,

(1) 8 V/m, towards (–x) axis

(2) Oscillate but not execute S. H. M. (3) Move towards origin and will become stationary. (4) S. H. M. along x axis. A charge q is placed in the middle of a line line joining the two equal and like point charges Q. This system will remain in equilibrium for which the value of q is (1) (3)

(2) 8 V/m, towards (+x) axis



Q

Q 2

3

(2)



Q

(4)



Q

4 2

A ball of mass 1g and charge 10 C moves from a point A (VA = 600 V) to the point B whose potential is zero. Velocity of the ball at the point B is 20 cm s –1. The velocity of the ball at the point A is –8

(3) 4 V/m, towards (–x) axis (4) 4 V/m, towards (+x) axis Two horizontal metal plates having a potential difference of 800 V are 0.02 m apart. A particle of mass 1.92 × 10 – 15 kg is suspended in equilibrium between the plates. If e is the elementary charge, then charge on the particle is : (1) e (2) 3e (3) 6e (4) 8e In Millikan's oil drop experiment, which of the following charges can be present on the oil drops – (1) 0.1e, charge equal to that on –particles (2) 2e, 1.6 x 10 –19 C (3) 2e, 1.6 x 10 –19 C, 2.5e (4) 1.5 e, e If V = a x y then electric field at a point proportional to (1) r

(2) r–1

Gauss law is given by 

(3) r–2

(4) r2

 E.ds = q, if net charge enclosed s

in Gaussian surface is zero then :–

(1) 16.7 ms –1

(2) 16.7 cm s–1

(3) 2.8 ms –1

(4) 2.8 cm s–1

If a charged spherical conductor of radius 10 cm has potential V at a point, distant 5 cm from its centre, then the potential at a point distant 15 cm from the centre will be : 3 V (1) 3V (2) 2 2 1 V V (3) (4) 3 3 There is a uniform electric field of strength 103 V/m along y–axis. A body of mass 1 g and charge 10–6 C is projected into the field from origin along the positive x –axis with a velocity 10m/s. Its speed in m/s after 10s is (Neglect gravitation) (1) 10

(2) 5 2

(3) 10 2

(4) 20

(1) E on surface must be zero (2) incoming and outgoing electric lines are equal (3) there is a net incoming electric lines (4) none

A uniform electric field pointing in positive x–direction exists in a region. Let A be the origin, B be the point on the x –axis at x = +1cm and C be the point





XI &XII (CBSE & ICSE BOARD) on the y –axis at y = +1 cm. Then the potentials at the points A, B and C satisfy. (1) VA < VB

(2) VA > VB

(3) VA < VC

(4) VA > VC

Choose correct statement regarding electric lines of force (1) Emerges from negative charge and meet at positive charge (2) Where the density of electric lines of force is more, the electric field in that region is weak. (3) It is in radial direction for a point point charge (4) Has a physical existence An elementary particle of mass m and charge +e is projected with velocity v at a much more massiveparticle of charge Ze, where Z > 0. What is the closest possible approach of the incident particle? (1)

(3)

Ze2 20 mv2 Ze2 80 mv

2

(2)

(4)

Ze 40 mv

2

Ze 80 mv

2

64 small drops of mercury, each of radius 'r' and charge q are combined to form a big drop. The ratio of the surface density of the charge of each small drop to that of a big drop is :– (1) 4 : 1

(2) 1 : 4

(3) 1 : 64

(4) 64 : 1

Three point charges are placed at the corners of an equilateral triangle. Assuming only electrostatics forces are acting– (1) if the charges have different magnitudes and different signs, the system will be in equilibrium. (2) the system will be in equilibrium if the charges have the same magnitudes but different signs. (3) the system can never be in equilibrium. (4) the system will be in equilibrium if the charges rotate about the centre of the triangle. Two copper balls, each having weight 10 g are kept in air 10 cm apart. If one electron from every 10 6 atoms is transferred from one ball to the other, the coulomb force between them is (atomic weight of copper is 63.5)

(1) 2.0 × 10 N

(2) 2.0 × 10 N

(3) 2.0 × 1010 N

(4) 2.0 × 104 N

8

How many times, the potential of big drop in comparison to small drops which is made of 8 droplets will be, if all the droplets are identical and having equal charge ? (1) 2 times (2) 4 times (3) 3 times (4) 8 times (–10–6) C charge is on a drop of water having mass 10–6 kg. What amount of electric field is applied on the drop so that it is in the balanced condition with its weight (1) 10 V/m upward

(2) 10 V/m downward

(3) 0.1 V/m downward

(4) 0.1 V/m upward

An electric dipole is placed in non uniform electric field, then it experiences (1) force must be zero (2) torque must be non zero (3) force must be non zero (4) both may be non zero What is the electric potential at a distance 'x' from the centre inside a conducting sphere which is charged upto Q and having radius R :– Q Q 1 1 (1) (2) 4 0 R 4 0 x (3)

1 4 0

x

(4) zero

An electron and a proton are set free in a uniform electric field. The ratio of their acceleration is: – (1) Unity (3)

mp me

(2) zero

(4)

me mp

Two point charges + 9e and +e are kept 16 cm. apart to each other. other. Where should a third charge q be placed between them so that the system remains in the equilibrium state :– (1) 24 cm from + 9e

(2) 12 cm from + 9e

(3) 24 cm from + e

(4) 12 cm from + e

When an electric dipole p is kept in a uniform electric field E then for what value of the angle between and p , E torque will be maximum :– (1) 90

(2) 0

(3) 180

(4) 45

6

Consider E 1 = x + y and E 2 = xy + x y then (1) only E is electrostatic (3) both are electrostatic


(2) only E is electrostatic (4) none

Identical charges (– q) are placed at each cornes of a cube of side 'b' then E.P.E. of charge (+ q) which is placed at centre of cube will be : (1)

 4 2 q2 0 b

(3)

 4 q2 30 b

(2)

 8 2 q2 0 b

(4)

8 2 q2 4 0 b





XI &XII (CBSE & ICSE BOARD) Some positive charge is given to a conductor. Then its potential :–


inertia is I. If the dipole is displaced then the angular frequency of its oscillation is 1

(1) is maximum at surface (1)

(2) is maximum at centre (3) remain same throughout the conductor

What will be the ratio of of electric electric field at the axis axis and and at equatorial line of a dipole : – (2) 2 : 1

(3) 4 : 1

(4) 1 : 4

(2)

(3)

 I 2  pE   

(4)

(1) (1 + 2)0

(1) Uniform

(3)

(2) Proportional to a distance from centre (4) Inversely proportional to square of distance A proton is accelerated through potential difference of 1 V then KE of proton will be : – (1) 1840 eV

(2) 0.1 eV

(3) 1 eV

(4)

1 1840

There is a neutral metallic sphere. Some one wants to develop 1 Faraday charge on it. How much number of electron has to removed from the sphere ? (1) 9 × 10

(2) 6.023 × 10

9

23

(3) 8.85  10

(4) 6 × 10

–12

(4)

2  1 0

(2) (3)

2Q 4 0 R

2Q 40 R

(4)

2Q 40 R

 

2q 4 0 R q 4 0 R

(2) N/C

(3) wb/m

(4) A/C

2

The potential at a distance R/2 from the centre of a conducting sphere will be Q (1) 0 (2) 8 0 R (3)

q  Q 2 4 0 R

18

Dimension of volt is equivalent to (1)J/C

1  2 0

(2) (2 – 1)0

A thin spherical conducting shell of radius R has a charge q. Another point charge Q is placed at the centre of the shell. The electrostatic potential at a point p a distance from the centre of the shell is

(1)

eV

 p 2    IE 

If the electric flux entering and leaving an closed surface respectively is 1 and 2 the electric charge inside the surface will be

Potential inside a hollow charged sphere is :–

(3) Inversely proportional to the distance

 pE  2  I    1

1

(4) is maximum somewhere between surface and centre

(1) 1 : 2

3

 pE  2  I   

Q 4 0 R

(4)

A hollow conducting sphere is placed in an electric field produced by a point charge placed at P as shown in figure. Let VA, V B, V C be the potentials at point A, B and C respectively. Then

A

Q 2 0 R

P

C B

Four charges +Q, –Q, +Q and –Q are situated on the corners of a square then at the centre of square (1) E=0, V=0 (2) E=0, V  0 (3) E  0, V=0 (4) E=0, V  0

(1) VC > VB

For a dipole q = 2 × 10 –6 C ; d = 0.01m find the maximum m aximum 5 torque on the dipole if E = 5 × 10 N/C

then value of

(1) 1 × 10–3 Nm–1

(2) 10  10–3 Nm–1

(1) 

(3) 10 × 10–3 Nm

(4) 1 × 102 Nm2

An electric dipole is situated in an electric field of uniform intensity E whose dipole moment is p and moment of

(2) VB > VC

(3) VA > VB

(4) VA = VC

Two particle particle of equal mass m and charge q are placed at a distance of 16 cm. Net force on each charge is zero

(3)

q m

is (2)

G 4 0

(4)

0 G

4 0 G







Three charges –q1 , +q2 and –q3 are placed as shown in the figure. The x–component of the force on –q1 is proportional to : y

–q3

a

(1)

–q1

(3)

q2 2

b q2 2

b

 

q3 2

a q3 a

2

sin  sin 

ˆ

(2) (4)

q2 2

b q2 b2

 

q3 a2 q3 a2

cos  (3) cos 

(2) –K

e r

2

2

3

r ˆ

2

e e (3) K 3 r (4) – K 3 r r r A charge q is placed at at the centre of a closed cub. The flux emitting from any one face of the cube will be Q Q (1) (2) 6 0 3 0

0

r

R

O

(2)

E

2

e (1) K 2 r r

Q

O

r

R

x

+q2

An electron electron is moving moving round the nucleus of a hydrogen atom in a circular orbit of radius r. The Coulomb force on the electron is

(3)

E

 b

(1)

E

(4)

O

r

R

O

(4)

r

R

Equipotential surface associated with an electric field which is increasing in magnitude along the x– direction, are (1) planes parallel to yz–plane (2) planes parallel to xy–plane (3) planes parallel to xz–plane (4) coaxial cylinders of increasing radii around the x –axis In the basic CsCl crystal structure, Cs+ and Cl– ions are arranged in a bcc configuration as shown below.The net electrostatic force exerted by the eight Cs + ions on the Cl – ion is Cs Cs

+

Cs

+

Cs

Q

+

+

a

Cl

–

4 0

Cs

An electric dipole has the magnitude of its charge as q and its dipole moment is p. It is placed in a uniform electric field E. If its dipole moment is along the direction of the field, the force on it and its potential energy are respectively :– (1) q. E and p. E (3) q. E and maximum

E

(2) zero and minimum (4) 2q. E and minimum

Conservation of charge is a consequence of (1) Columb law (2) Gauss law (4) Huygen’s wave equation (3) Continuity equation Which statement is not correct for a conducting charged sphere – (1) electric field inside the sphere is not equal to zero (2) V is constant inside the sphere (3) the direction of E is radial outside the sphere (4) charge density inside the sphere is zero When charge is given to a soap b ubble, it shows (1) an increase in size (2) sometimes an increase and sometimes a decrease in size (3) no change in size (4) none of these The electric field due to to a uniformly charged sphere of radius R as a function of the distance from its centre is represented graphically by

Cs

+

(1) zero (3)

+

Cs a

+

Cs

(2)

1

32e

4  0

3a

2

2

+

(4)

1

16e

4  0

3a

1

4e

2

2

2

4  0 3a 2

Using mass (M), length (L), time (T) and current (A) as fundamental quantities, the dimension of permittivity is (1) ML –2T2A

(2) M–1 L –3 T4 A2

(3) MLT–2A

(4) ML 2T–1A2

In an electric field electric dipole is rotated though an angle ,then work done will be (1) pE(1 – cos) (2) pE sin (3) zero (4) – pE cos  An isolated conducting sphere of radius r has given a charge q, then its P.E. will be : (1) (3)

q2 4  0 r

q 8 0 r

(2) (4)

q

2

2 0 r q2 8 0 r







An electron travels a distance of 0.10 m in an electric field of intensity 3200 V/m, enters perpendicular to the field with a velocity 4  107m/s, what is its deviation in its path (1) 1.76 mm. (3) 176 mm.

(2) 17.6 mm. (4) 0.176 mm.

Two concentric conducting thin spherical shells A, and B having radii rA and rB (rB > r A) are charged to QA and –QB (|QB| > |QA|). The electrical field along a line, (passing through the centre) is:

Two charges q1 and q2 are placed 30cm apart, as shown in the figure. C

q3

(1)

(2)

(3)

(4)

40cm q1 A

q2 30cm

BD

A third charge q3 is moved along the arc of a circle of radius 40cm from C to D. The change in the potential q3 energy of the system is k , where k is 4 0 (1) 8q2 (3) 8q1

A square surface of side L metre is in the plane of of the the paper. A uniform electric field E (volt/m), also in the plane of the paper, is limited only to the lower half of the square surface, (see figure). The electric flux in SI units associated with the surface is

(2) 6q2 (4) 6q1

As per this diagram a point point charge +q is placed at the origin O. Work done in taking another point charge –Q from the point A [coordinates (0, a)] to another point B [coordinates(a,0)] along the straight path AB is

E

(1) zero

(2) EL 2

2

y

(3)

EL

2 0

(4)

EL 2 2

A

O (1) ( (3) (

qQ 4  0 qQ

1 a

2

)

1

4 0 a 2

x

B

2 a 1 2

An electric dipole of dipole moment is lying along a uniform electric field . The work done in rotating the dipole by 90 is :– (1) 2pE (2) pE pE (3) 2pE (4) 2

(2) zero (4) (

qQ

1

4  0 a2

)

2a

Two infinitely long parallel conducting plates having surface charge densities + and –  respectively on inner faces are separated by a small distance. The medium between the plates is vacuum. If 0 is the dielectric permittivity of vacuum, then the electric field in the region between the plates is (1) 0 volt/meter (3)

 0

volt/meter

(2) (4)

 volt/meter 2 0 2 volt/meter 0

Two parallel large thin metal sheets have equal surface charge densities( = 26·4 × 10 –12 C/m 2) of opposite signs. The electric field between these sheets is (1) 1·5 N/C (2) 1·5 × 10–10 N/C (3) 3 N/C

(4) 3 × 10–10 N/C

Two charges are +2µC and –5µC. Find the ratio of forces acting on each, is : – (1) 2 : 5 (2) 5 : 2 (3) 1 : 1 (4) 4 : 25 Charges +q and –q are placed at points A and B respectively which are a distance 2L apart, C is the mid point between A and B. The work done in moving a charge +Q along the semicircle CRD is : –






Three concentric spherical shells have radii a, b and c(a < b < c) and have surface charge densities , – and  respectively. If V A, VB and VC denote the potentials of the three shells, then, for c = a+ b, we have [

R A (1) (3)



qQ 6 0 L qQ

2 0 L

C

B (2)

(4)


D qQ

(1) VC = VB = VA

(2) VC = VA  VB

4  0 L

(3) VC = VB  VA

(4) VC  VB  VA

qQ 6 0 L

A hollow cylinder has a charge q coulomb within it. If  is the electric flux in units of voltmeter associated with the curved surface B, the flux linked with the plane surface A in units of voltmeter will be

Two positive ions, each carrying a charge q, are separated by a distance d. If F is the force of repulsion between the ions, the number of electrons missing from each ion will be (e being the charge on an electron) (1)

B

(3) C

(1) (3)

q

0

(2)

(4)

2 0

q2 d2

(2)

    2 0  

3

(2)

2 qa along + y direction

(3)

2 qa along the line joining points

e2 4  0 Fd2

(4)

e2

E

Three point charges +q, –2q and +q are placed at points (x = 0, y = a, z = 0),(x = 0, y = 0, z = 0) and (x = a, y = 0, z = 0) respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are 2 qa along + x direction

2

A square surface of side L meter in the plane of the paper is placed in a uniform electric field E (volt/m) acting along the same plane at an angle  with the horizontal side of the square as shown in figure. The electric flux linked to the surface, in units of volt –m, is

1 q

(1)

4 0 Fd

2

4  0 Fe 2

A



q

4 0 Fd

(x = 0, y = 0, z = 0) and (x = a, y = a, z = 0) (4) q a along the line joining points (x = 0, y = 0, z = 0) and (x = a, y = a, z = 0) The electric potential at a point in free space due to a charge Q coulomb is Q × 10 11 volts. The electric field at that points is :-



(1) Zero

(2) EL 2

(3) EL 2cos

(4) EL 2sin

The electric field at a distance

3R

from the centre of a 2 charged conducting spherical shell of radius R is E. The R electric field at a distance from the centre of the 2 sphere is E E (1) E (2) (3) (4) Zero 2 3

(1) 40 Q × 1020 volt/m A charge Q is enclosed by a Gaussian spherical surface of radius R. If the radius is doubled, then the outward electric flux will :-

(2) 120 Q × 1022 volt/m (3) 40 Q × 1022 volt/m (4) 120 Q × 1020 volt/m The electric potential at a point (x, y, z) is given by: V = –x2y – xz3 + 4 The electric field E at that point is : 3z2x (1) E = ̂(2xy (2xy – z3) + ̂ xy2 + 

 3xz2 (2) E = ̂ (2xy (2xy + z 3) + ̂ x2 +   (3xz – y2) (3) E = ̂2xy 2xy + ̂ (x2 + y2) +   z2 (4) E = ̂z3 + ̂ xyz + 

(1) Increase four times (2) Be reduced to half (3) Remain the same (4) Be doubled Four electric charges + q, +q, – q and – q are placed at the corners of a square of side 2L(see figure). The electric potential at point A, midway between the two charges +q and +q, is ELECTROSTATICS FORCE & FIELD




XI &XII (CBSE & ICSE BOARD) +q


for which the potential at the centre of the square is zero is : 1 (1) Q = q (2) Q = q

–q

A

+q

(1)

(3)

1

2q

4  0 L 1

(3) Q = –q

–q

 1 (2)   4  0 L  5 1

(1  5 )

2q 

  5

1

1  4  0 L 

2q 

(4) Q =



1 q

1

Two metallic spheres of radii 1 cm and 3 cm are given charges of – 1 × 10 –2 C and 5 × 10 –2 C, respectively. If these are connected by a conducting wire, the final charge on the bigger sphere is (1) 4 × 10–2 C (2) 1 × 10–2 C (3) 2 × 10–2 C (4) 3  10–2 C

(4) Zero

Three charges each +q are placed at the corners of an isosceles triangle ABC of sides BC and AC, 2a. D and E are the mid points of BC and CA. The work done in taking a charge Q from D to E i s A

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

(2) 8 along positive X-axis

31

32

33

34

35

(3) 16 along negative X-axis

36

37

38

39

40

41

42

43

44

45

What is the the flux through a cube of side 'a' if a point charge of q is at one of its corner : q q 2q q 2 (1) (2) (3) (4) 6a 0 0 2 0 8 0

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

An electrical dipole of moment 'p' is placed in an electric field of intensity 'E'. The dipole acquires a position such that the axis of the dipole makes an angle  with the direction of the field. Assuming that the potential energy of the dipole to be zero when  = 90 , the torque and the potential energy of the dipole will respectively be :-

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

(2) p E cos , –p E sin 

86

87

88

89

90

(3) p E sin , –p E cos 

91

92

93

94

95

96

97

98

99

100

E

B

(1)

3qQ 4  0 a

(2)

C

D

3qQ 8 0 a

(3)

qQ 4  0 a

(4) Zero

The electric potential V at any point (x, y, z), all in meters in space is given by V = 4x2 volt. The electric field at the point (1, 0, 2) in volt/meter, is :(1) 8 along negative X-axis

(4) 16 along positive X-axis

(1) p E sin , 2p E cos 

(4) p E sin , –2p E cos  Four point charges –Q, –q, 2q and 2Q are placed, one at each corner of the square. The relation between Q and q




100 Question 100 Min. Series Electrostatics

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