ELECTROSTATICS 1.
Mid way between the tow equal and similar charges, we placed the third equal and similar charge. Which of the following statements is correct, concerned to the equilibrium along the line joining the charges ? (a) The third charge experiences a net force inclined to the line joining the charges. (b) The third charge is in stable equilibrium. (c) The third charge is in unstable equilibrium. (d) The third charge experiences a net force perpendicular to the line joining the charges.
2.
A negative point charge placed at the point A is (a) In stable equilibrium along x-axis. (b) In unstable equilibrium along x-axis. (c) In stable equilibrium along y-axis. (d) In unstable equilibrium along x-axis.
a +2q
a A
+2q
3.
Five balls numbered 1 to 5 are suspended using separate threads. Pairs (1, 2), (2, 4) and (4, 1) show electrostatic attraction while pairs (2, 3) and (4, 5) show repulsion. Therefore ball 1 must be (a) Positively charged (b) Negatively charged (c) Neutral (d) Made of metal.
4.
Four charges of 1C, 2C, 3 C and -6 C are placed one at each corner of the square of side 1m. The square lies in the x-y plane with its centre at the origin. (a) The electric potential is zero at the origin. (b) The electric potential is zero everywhere along x-axis of the sides of the square are parallel to x and y axis. (c) The electric potential is zero everywhere along the z-axis for any orientation of the square in the x-y plane. (d) The electric potential is not zero along the z-axis except at the origin.
5.
–Q Two fixed charges 4Q (positive) and Q (negative) are located at A + 4 q and B, the distance AB being 3m. A B 3m (a) The point P where the resultant field due to both is zero is on AB outside AB. (b) The point P where the resultant field due to both is zero is on AB inside AB. (c) If a positive charge is placed at P and displaced slightly along AB it will execute oscillations. (d) If a negative charge is placed at P and displaced slightly along AB it will execute oscillations.
6.
Two identical charges +Q are kept fixed some distance apart. A small particle P with charge q is placed midway between them. If P is given a small displacement , it will undergo simple harmonic motion if (a) q is positive and is along the line joining the charges. (b) q is positive and is perpendicular to the line joining the charges. (c) q is negative and is perpendicular to the line joining the charges. (d) q is negative and is along the line joining the charges.
7.
Select the correct statement : (Only force on a particle is due to electric field)
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(a) (b) (c) (d)
A charged particle always moves along the electric line of force. A charged particle may move along the line of force. A charged particle never moves along the line of force. A charged particle moves along the lien of force only if released from rest.
8.
Q – Q /4 3m Two point charges Q and –Q/4 are separated by a distance x. Then (a) Potential is zero at a point on the axis which is x/3 on the right side of the charge –Q/4. (b) Potential is zero at a point on the axis which is x/5 on the left side of the charge –Q/4. (c) Electric field is zero at a point on the axis which is at a distance x on the right side of the charge –Q/4. (d) There exist two points on the axis where electric field is zero.
9.
An electric charge 10-8 C is placed at the point (4m, 7m, 2m). At the point (1m, 3m, 2m), the electric (a) Potential will be 18 V (b) Field has no Y-component (c) Field will be along Z-axis (d) Potential will be 1.8 V.
10.
Let V be electric potential and E the magnitude of the electric field. At a given position, which of the statement is true ? (a) E is always zero where V is zero (b) V is always zero where E is zero (c) E can be zero where V is non zero (d) E is always nonzero where V is nonzero.
11.
Three point charges Q, 4Q, and 16Q are placed on a straight line 9 cm long. Charges are placed in such a way that the system has minimum potential energy. Then (a) 4Q and 16 Q must be at the ends and Q at a distance of 3 cm from the 16 Q. (b) 4Q and 16 Q must be at the ends and Q at a distance of 6 cm from the 16 Q. (c) Electric field at the position of Q is zero. Q (d) Electric filed at the potion of Q is . 40
12.
Two infinite sheets of uniform charge density + and - are parallel to each other as shown in the figure. Electric field at the (a) Points to the left or to the right of the sheets is zero. (b) Midpoint between the sheets is zero. (c) Midpoint of the sheets is /0 and is directed towards right. (d) Midpoint of the sheets is 2/0 and is directed towards right.
13.
14.
+
+ + + + + + + +
– – – – – – – – –
The electric potential decreases uniformly from V to –V along X-axis in a coordinate system as we moves from a point (-x0, 0) to (x0, 0), then the electric field at the origin. V V (a) Must be equal to (b) May be equal to x0 x0 V V (c) Must be greater than (d) May be less than . x0 x0
The electric potential decreases uniformly from 120 V to 80 V as one moves on the X-axis from x = - 1 cm to x = + 1 cm. The electric field at the origin (a) Must be equal to 20 V/cm (b) May be equal to 20 V/cm (c) May be greater than 20 V/cm (d) May be less than 20 V/cm. PARTHIITJEE
15.
Potential at a point A is 3 volt and at a point B is 7 volt, an electron is moving towards A from B. (a) It must have some K.E. at B to reach A. (b) It need not have any K.E. at B to reach A. (c) To reach A it must have more than or equal to 4eV K.E. at B. (d) When it will reach A, it will have K.E. more than or at least equal to 4 eV if it was released from rest at B.
16.
A ring of radius R carries charge Q distributed uniformly over the ring. P is a point on its axis, at a distance r from its centre. The electric field at P due to ring is E. Which of the following is correct ? 1 Qr . 2 (a) E . 40 (r R 2 )3 / 2 (b) E is maximum for r R / 2 . (c) E 0 at the centre of the ring. (a) As r increases, E will first increase, the decrease.
17.
A conducting sphere or radius r has a charge. Then (a) The charge is uniformly distributed over its surface, it there is an external electric field. (b) Distribution of charge over its surface will be non uniform if no external electric field exist in space. (c) Electric field strength inside the sphere will be equal to zero only when no external electric field exists. (d) Potential at every point of the sphere must be same.
18.
For a spherical shell (a) If potential inside it is zero then it necessarily electrically neutral. (b) Electric field in a charged conducting spherical shell can be zero only when the charge is uniformly distributed. (c) Electric potential due to induced charges at a point inside it will always be zero. (d) None of these.
19.
A circular ring carries a uniformly distributed positive charge. The electric field (E) and potential (V) varies with distance (r) from the centre of the ring along its axis as E
E
(a)
(b) r
r
E
E
(c)
(d) r
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. r
20.
+ The figure shows a non-conducting ring which has positive and + negative charge non uniformly distributed on it such that the total + charge is zero. Which of the following statement is true ? O (a) The potential at all the points on the axis will be zero. + (b) The electric field at all the points on the axis will be zero. + (c) The direction of electric field at all points on the axis will be along the axis. (d) If the ring is placed inside a uniform external electric field then net torque on the ring would be zero.
– – – – –
a x is
and force acting
21.
At distance of 5 cm and 10 cm outwards from the surface of a uniformly charged solid sphere, the potentials are 100 V and 75 V respectively. Then (a) Potential at its surface is 150V. (b) The charge on the sphere is (5/3) × 1-10 C. (c) The electric field on the surface is 1500 V/m. (d) The electric field at its center is 225 V.
22.
Four identical charges are place at the points (1, 0, 0), (0, 1, 0), (-1, 0, 0) and (0, -1, 0). (a) The potential at the origin is zero. (b) The field at the origin is zero. (c) The potential at all points on the z-axis, other than the origin, is zero. (d) The field at all points on the z-axis, other than the origin acts along the z-axis.
23.
Variation of electrostatic potential along x-direction is shown in the graph. The correct statement about electric field is (a) x component at point B is maximum. (b) x component at point A is towards positive x-axis. (c) x component at point C is along negative x-axis. (d) x component at point C is along positive x-axis.
v A
B
C
x
24.
A particle of charge 1 C & mass 1 gm moving with a velocity of 4 m/s is subjected to a uniform electric field of magnitude 300 V/m for 10 sec. Then it’s final speed cannot be (a) 0.5 m/s (b) 4 m/s (c) 3 m/s (d) 6 m/s.
25.
The point charges q and 2q are placed at (a, 0) and (0, a). A point charge q1 is placed at a point P on the quarter circle of radius a as shown in the diagram so that electric field at the origin becomes zero a 2a , (a) The point P is . 3 3
(b) The point P is
(c) q1 = -5q . (d) None of these.
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a 2a , . 5 5
2q
P
a O
a
q
26.
A charged cork of mass m suspended by a light string is placed in uniform electric field of strength E = (iˆ ˆj) × 105NC-1 as shown in the figure. If the equilibrium position tension in the string is 2 mg then angle with the vertical is (1 3) (a) 60° (b) 30° (c) 45° (d) 18°.
E
27.
Two particles of same mass and charge are thrown in the same direction along the horizontal with same velocity v from two different heights h1 and h2 (h1 < h2). Initially they were located on the same vertical line. Choose the correct alternative. (a) Both the particles will always lie on a vertical line (b) Acceleration of the centre of mass of two particles will be g downwards (c) Horizontal displacement of the particle lying at h1 is less and the particle lying at h2 is more than the value, which would had been in the absence of charges on them (d) All of these
28.
A proton and a deuteron are initially at rest and are accelerated through the same potential difference. Which of the following is false concerning the final properties of the two particles? (a) They have different speeds (b) They have same momentum (c) They have same kinetic energy (d) They have been subjected to same force.
29.
A particle of charge – q and mass m moves in a circle around a long wire of linear charge density + . If r = radius of the circular path T = time period of the motion circular path. Then (a) T = 2 r (m/2Kq)1/2 (b) T2 = 42 mr3/2qK (c) T = 1/2r (2Kq/m)1/2 (d) T = 1/2r(m/Kq)1/2 where K = 1/40.
30.
Charge Q is distributed non-uniformly over a ring of radius R, P is a point on the axis of ring at a distance 3 R from its centre. Which of the following is a wrong statement. KQ (a) Potential at P is . 2R 3 KQ (b) Magnitude of electric field at P may be greater than . 8R 2 3 KQ (c) Magnitude of electric field at P must be equal to . 8R 2 3 KQ (d) Magnitude of electric field at P cannot be less than . 8R 2
31.
r An electric dipole moment p (2.0iˆ 3.0ˆj) C. m is placed in a uniform electric field r ˆ × 105 NC-1. E (3.0iˆ 2.0k) r r (a) The torque that E exerts on p is (0.6 ˆi - 0.4 ˆj - 0.9 kˆ ) Nm. (b) The potential energy of the dipole is 0.6 J (c) The potential energy of the dipole is 0.6 J (d) If the dipole is rotated in the electric field, the maximum potential energy of the dipole is 1.3J.
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32.
Which of the following is true for the figure showing electric lines of force? (E is electric field, V is potential) (a) EA > EB (b) EB > EA (c) VA > VB (d) VB > VA.
A
B
33.
If we use permittivity , resistance R, gravitational constant G and voltage V as fundamental physical quantities, then (a) [angular displacement] = 0 R°G°V° (b) [velocity] = -1 R-1G°V° (c) [dipole momentum]1R°G°V1 (d) [force] = 1R°G°V2.
34.
Units of electric flux are N m2 (a) coul 2 (c) Volt – m
N Coul 2 m (d) Volt – m3. (b)
35.
Which of the following statements are correct? (a) Electric field calculated by Gauss law is the field due to only those charges which are enclosed inside the Gaussian surface. (b) Gauss law is applicable only when there is a symmetrical distribution of charge. (c) Electric flux through a closed surface will depends only on charges enclosed within that surface only. (d) None of these.
36.
Mark the correct options: (a) Gauss’s law is valid only for uniform charge distributions. (b) Gauss’s law is valid only for charges placed in vacuum. (c) The electric field calculated by Gauss’s law is the field due to all the charges. (d) The flux of the electric field through a closed surface due to all the charges is equal to the flux due to the charges enclosed by the surface.
37.
A thin-walled, spherical conducting shell S of radius R is given charge Q. The same amount of charge is also placed at its centre C. Which of the following statements are correct? Q (a) An the outer surface of S, the charge density is . 2 R 2 (b) The electric field is zero at all points inside S. (c) At a point just outside S, the electric field is double the field at a point just inside S. (d) At any point inside S, the electric field is inversely proportional to the square of its distance from C.
38.
A hollow closed conductor of irregular shape is given some charge. Which of the following statements are correct? (a) The entire charge will appear on its outer surface. (b) All points on the conductor will have the same potential. (c) All points on its surface will have the same charge density. (d) All points near its surface and outside it will have the same electric intensity.
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39.
Charge Q1 and Q2 lies inside and outside respectively of a closed surface S. Let E be the field at any point on S and be the flux of E over S. (a) If Q1 changes, both E and will change. (b) If Q2 changes, E will change but will not change. (c) If Q1 = 0 and q2 0 then E 0 but = 0. (d) If Q1 0 and Q2 = 0 then E = 0 but 0.
40.
Three points charges are placed at the corners of an equilateral triangle of side L as shown in the figure. (a) The potential at the centroid of the triangle is zero. (b) The electric field at the centroid of the triangle is zero. (c) The dipole moment of the system is 2 qL. (d) The dipole moment of the system is 3qL .
L
+q
L
L
–2Q
41.
An electric dipole is placed at the centre of a sphere. Mark the correct answer (a) the flux of the electric field through the sphere is zero (b) the electric field is zero at every point of the sphere (c) the electric potential is zero everywhere on the sphere (d) the electric potential is zero on a circle on the surface
42.
An electric field converges at the origin whose magnitude is given by the expression E = 100rNt/Coul, where r is the distance measured from the origin. (a) Total charge contained in any spherical volume with its centre at origin is negative. (b) Total charge contained at any spherical volume, irrespective of the location of its centre, is negative. (c) Total charge contained in a spherical volume of radius 3 cm with its centre at origin has magnitude 3 10–13C. (d) Total charge contained in a spherical volume of radius 3 cm with its centre at origin has magnitude 3 10–9 Coul.
43.
B A conducting sphere A of radius a, with charge Q, is placed A Q concentrically inside a conducting shell B of radius b. B is a earthed. C is the common centre of the A and B 1 Q (a) The field is distance r from C, where a r b is . 40 r 2 b (b) The potential at a distance r from C, where a r b, is 1 Q . 40 r 1 1 1 Q . (c) The potential difference between A and B is 40 a b 1 1 1 Q . (d) The potential at a distance r from C, where a r b, 40 r b
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44.
45.
46.
47.
48.
Q
Three concentric conducting spherical shells radius r, 2r and 3r and Q1 and Q3 are final charges respectively. Innermost and outermost shells are already earthed as shown in figure. Choose the wrong statement. Q 2 (a) Q1 + Q3 = –Q3 (b) Q1 4 Q3 Q 3 1 3 . (c) (d) Q1 Q1 3
2 1
r
Two thin conducting shells of radii R and 3R are shown in the figure. The outer shell carries a charge + Q and the inner shell is neutral. The inner shell is earthed with the help of a switch S. (a) With the switch S open, the potential of the inner sphere is equal to that of the outer. (b) When the switch S is closed, the potential of the inner sphere becomes zero. (c) With the switch S closed, the charge attained by the inner sphere is –q/3. (d) By closing the switch the capacitance of the system increases.
3R
R
X
X and Y are large, parallel conducting plates closed to each other. Each face has an area A. X is given a charge Q. Y is without any charge. Points A, B and C are as shown in figure. Q (a) The field at B is . 2 0 A Q (b) The field at B is . 0 A (c) The fields at A, B and C are of the same magnitude . (d) The field at A and C are of the same magnitude, but in opposite directions. Plates A and B constitute an isolated, charge parallel-plate capacitor. The inner surfaces (I and IV) of A and B have charges +Q and –Q respectively. A third plate C with charge +Q is now introduced correct? (a) The surfaces I and II will have equal and opposite charges. (b) The surfaces III and IV will have equal and opposite charges (c) The charge on surfaces III will be greater than Q. (d) The potential difference between A and C will be equal to the potential difference between C and B.
Q Q
3r
3
S
Y
B
A
A
C
C
B –Q
+Q
I
II
III
IV
A particle of mass m and charge q is thrown in a region where uniform gravitational field and electric field are present. The path of particle (a) May be straight line (b) May be a circle (c) May be a parabola (d) May be a hyperbola.
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+ b
–
a
– –
– –
– +
+
+
+
+
+
+
Question No. 49 to 50 An empty thick conducting shell of inner radius a and outer radius b is shown in figure. If it is observed that the inner face of the shell carries a uniform charge density - and the surface carries a uniform charge density .
49.
If a point charge qA is placed at the centre of the shell, then choose the correct statement(s) (a) The charge must be positive. (b) The charge mast be negative. (c) The magnitude of charge must be 4a2. (c) The magnitude of charge must be 4(b2 - a2).
50.
If another point charge qB is also placed at a distance c (>b) the centre of shell, then choose the correct statement q A b 2 (a) Force experienced by charge A is . 0c2 (b) Force experienced by charge A is zero. q B b 2 (c) The force experienced by charge B is . 0c 2 kq A q B (d) The force experienced by charge B is . c2 ANSWER KEYS (ELECTROSTATICS)
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22.
b c, d c, d a, c a, d a, c b a, b, c a c b, c a, c b b, c a, c a, b, d d d b a a, c, d b, d
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23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50.
d a b a, b d b a c a, b, d a, d a, b, d c c c, d a, c, d a, b a, b, c a, d a, d a, b, c a, c, d d a, b, c, d a, c, d d a, c a, c b
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