ASSIGNMENT ELECTROMAGNETISM (ADVANCED) PART -1 SINGLE CORRECT CHOICE TYPE
1.
A current carrying square loop is placed near an infinitely long current carrying wire as shown in figure. The torque acting on the loop is
0 i1 i2a 2 2
2.
0 i1 i2 a ln(2) 2
a) b) c) d) zero A conducting ring of radius R, mass M and carrying current I in anticlockwise direction as seen from top hangs, with its plane parallel to horizontal plane, by two non-conducting strings as shown in the figure. The uniform horizontal magnetic field B exists is the region. If both strings are tight and the ring is in equilibrium, find the minimum tension in the any string.
2 IRB Mg a) 3.
0 i1 i2 a 2
2
Mg b) 2
IπRB Mg
Mg π IRB
2 2 c) d) A current carrying wire carries a current of 2A, which is out of the page, another wire carrying current of 4A in same direction lies parallel to the first, as shown in figure. Then around which loop linking both the wires
4A 2A
2A4A
r r
òB.dl will be zero?
a)
b)
4A 2A
2A4A 4.
c) d) A particle with charge Q, moving with a momentum p, enters a uniform magnetic field normally. The magnetic field has magnitude B and is d
p BQ . The particle is deflected
confined to a region of width d, where by a total angle in travelling through the field. Then:
Q
p
x
x
x
x
x
x
x
x
x
x
x
x
d
a)
sin
BQd p
b)
sin
p BQd
c)
sin
Bp Qd
d)
sin q =0
5.
Infinite number of straight wires each carrying current I are equally placed as shown in the figure. Adjacent wires have current in opposite direction. Net magnetic field at point P due to the segments of the wires indicated in the figure is:
a) 6.
0 I 1n 2 ˆ k 4 3a
b)
0 I 1n4 ˆ k 4 3a
c)
0 I 1n 4 ˆ k 4 3a
d) Zero
A direct current is passing through a wire of a given length. It is bent to form a coil of one turn. Now it is further bent to form a coil of two turns
but of smaller radius. The ratio of the magnetic induction at the centre of the coil of two turns and at the centre of the coil of one turn is: a) 1 : 8 7.
b) 8 : 1
c) 4 : 1
d) 1 : 1
A long straight metal rod has a very long hole of radius a drilled parallel to the rod axis as shown in the figure. If the rod carries a current i uniformly, find the magnitude of magnetic induction on the axis of the hole, where OC=c
acO b
0ic 2 b 2 a 2
0ic b2 a 2
8.
)
0ic 2 2 2pabc a) b) c) d) 2 a b A long straight wire, carrying current I is bent at its midpoint to form an angle of 45°. Induction of magnetic field at point P, distant R from point of bending is equal to:
a) 9.
(
m0i b 2 - a 2
4500I P R
2 1 0 I 4 R
b)
2 1 0 I 4 R
c)
2 1 0 I 4 2 R
d)
2 1 0 I 4 2 R
r ˆ B A uniform magnetic field B0 j exists in a space. A particle of mass m
and charge q is projected towards negative x axis with speed v from a point d ,0,0 . The maximum value of v for which the particle does not hit y z plane is:
2Bqd a) m
Bqd b) m
Bq c) 2dm
Bqd d) 2m
10. In figure, a light coil of single turn is wound on a sphere of radius r and mass m . The plane of the coil is parallel to the smooth inclined plane and lies in the equatorial plane of the sphere. For the sphere to be in rotational
O B m g
equilibrium the magnitude of magnetic field B is, [Current in the coil is I]
mg a) Ir
mg sin b) I
mg cos c) I
d) zero
MULTIPLE CORRECT CHOICE TYPE
11.
A particle of charge and mass m enters normally (at point P) in a region of magnetic field with speed v . It comes out normally from Q after time T as shown in figure. The magnetic field B is present only in the region of radius R and is uniform. Initial and final velocities are along radial direction and they are perpendicular to each other. For this to happen, which of the following expression(s) is /are correct?
B vR vQ P
a)
c) 12.
R 2v
B
mv qR
b)
T
m 2qB
mv B= 2qR d)
T
Charge particle of charge q and mass m is moving with velocity v as shown in figure in a uniform magnetic field B along – ve z-direction. Select the correct alternative (s) :
y300x qv.m
x x x x x
x x x x
x x x x x x
x x x x x x x
x x x x x x x x
x x x x x x x x x
Extend upto a large distance
a) Velocity of the particle when it comes out from the magnetic field is r V v cos 60iˆ v sin 60 ˆj m b) Time for which the particle was in magnetic field is 3qB
mv c) Distance travelled in magnetic field is 2qB pm d) Time for which the particle was in magnetic field is qB 13.
r ˆ V a A charged particle of specific charge moves with a velocity =v0i in a r B B = 0 ˆj +kˆ 2 magnetic field then
(
)
a) Path of the particle is a helix
b) Path of the particle is circle p v0 t= B0a is B0 a c) Distance moved by the particle in time t
14.
v0 ˆ v0 i B0 is 2 2
ˆj
d) Velocity of the particle after time r A particle of charge q and mass m enters a uniform magnetic field B (perpendicular to paper inward) at P with a velocity v0 at an angle and leaves the field at Q with velocity v at angle as shown in figure:
B v
x
x
P x
x
x
x
x
x
x
x
x
x
x
x
x
v0
Q
a)
b) v v0
c)
PQ
t
2mv0 sin Bq
2m Bq
d) The particle remains in the field for time 15. Two long, identical bar magnets are placed under a horizontal piece of paper,as shown in figure. The paper is covered with iron filings. When the two north poles are a small distance apart and touching the paper, the iron filings move into a pattern that shows the magnetic lines of forces. Which of the following best illustrates the pattern that results?
1)
2)
3)
4)
INTEGER ANSWER TYPE
16.
An electron moves through a uniform magnetic field given r B = Bxiˆ +( 3Bx ) ˆj T . At a particular instant, the electron has the
(
velocity
( 6.4 ´ 10 17.
)
r v 2.0iˆ 4.0 ˆj m / s –19
)
N kˆ
and the magnetic force acting on it is
Find Bx .
A very long wire carrying a current I =5.0A is bent at right angles. Find the magnetic induction (in multiples of 10-6T) at a point lying on a normal to the plane of the wire drawn through the point of bending at a distance l 35cm from it.
18.
A current I 2 A flows in a circular having the shape of isosceles trapezium. The ratio of the bases of the trapezium is 2. Find the magnitude of magnetic induction B (in multiples of 10-6T) at symmetric point O in the plane of the trapezium. The length of the smaller bases of the trapezium is 100 mm and the distance r = 50 mm.
19.
A wire carrying a finite current in it has the configuration as shown in figure. Two semi-infinite straight sections, both tangent to the same circle, are connected by a circular arc of central angle θ , along the circumference of the circle, with all sections lying in the same plane. What must (in radian) be for magnitude of magnetic field to be zero at the centre of the circle?
20.
Consider the three long, straight, parallel wires as shown in figure. Find the magnitude of force (in multiples of 10-4N) experienced by a 25cm length of wire C.
KEY 1) D 2) D 3) A 4) D 5) B 6) C 7) B 12) A, B 13) B, C or B
8) A 9) B 10) D11) A,B,C
14) A, B, C, D 15) B
16) 2 17) 2 18) 2
19) 2 20 ) 3 PART -2 SINGLE CORRECT CHOICE TYPE
1.
A square coil of side a carrying current I and is having one of its side AB parallel to y-axis and its plane is at angle q=30° with x-axis (as shown). If a uniform magnetic field B exists in the region along kˆ direction, then torque due to magnetic force on the coil is:
Ia 2 B ˆ j a) 2
2.
(
)
Ia 2 B ˆ ˆ k +j c) 2
(
)
Ia 2 B ˆ i d) 2
Y aP bcx
For c=2a and a < b < c, the magnetic field at point P will be zero when [the figure is in the x-y plane]
a) a b 3.
Ia 2 B ˆ ˆ - k +j b) 2
3 a b 5 b)
r
5 a b 3 c)
1 a b 3 d)
ˆ ˆ A particle is moving with velocity v =i +3 j and it produces an electric
r E field at a point given by =2kˆ . It produces a magnetic field at that point
equal to (all quantities are in S.I. units) 6iˆ - 2 ˆj 2 a) c
6iˆ +2 ˆj 2 b) c
d) Cannot be determined from the given data
c) zero
4.
A wire of cross section area A forms three sides of a square and is free to rotate about OO¢. If the structure is deflected by and angle ' ' from the vertical when current i is passed through it in a magnetic field B acting vertically upwards and density of the wire is e then the value of is
B o1 O
5.
2 Aeg cot iB a)
2 Aeg tan iB b)
2 Aeg sin c) iB
Aeg cos d) iB
Two long cylinders (with axis parallel) are arranged as shown to form overlapping cylinders, each of radius r, whose centers are separated by a distance d. Current of density J (Current per unit area) flows into the plane of page along the right shaded part of one cylinder and an equal current flows out of the plane of the page along the left shaded part of the other, as shown. The magnetic field at point O is (O is the origin of shown x-y axes)
m0 Jd a) of magnitude 2 ,in the + y direction m0 Jd 2 b) of magnitude 2r , in the + y direction m0 Jd 2 c) of magnitude 2r , in the – y direction
d) zero 6.
Two parallel conducting rods are placed such that these form an incline as shown in figure. Another rod of mass m and length l equal to the separation between the two rods is placed on the incline and slides down without friction. If a uniform magnetic field B directed vertically downward exists at the place, what constant current should be passed through the sliding rod, such that it slides down with constant velocity?
iB
mg tan lB a)
7.
mg cos lB b)
mg sin c) lB
mg d) lB
An infinite current carrying wire is placed along x-axis such that it lies between x = 0 to x ® +¥ (infinity). The current is in direction of positive x-axis. Let B1, B2 and B3 be the magnitude of magnetic field at points A(a, a), B(0, a) and C(–a, a) respectively. Then pick the incorrect option. a) B1 >B2 >B3
b) B1 : B2 : B3 = 2 +1:1: 2 - 1
B2 =
8.
B1 B3 1 = 2 B 2 2 d)
B1 +B3 2
c) Two thin long parallel wires separated by a distance b are caring a current i each. The magnitude of the force per unit length exerted by one wire on the other is m0i 2 2 a) pb
m0i 2 b) 2pb
m0i c) 2pb
m0i 2 d) 2pb
Paragraph Type
passage - I A conducting ring of mass m and radius r has a weightless conducting rod PQ of length 2r and resistance 2R attached to it along its diameter. It is pivoted at its center C with its plane vertical, and two blocks of mass m and 2m are suspended by means of a light in-extensible string passing over it as shown in figure. The ring is free to rotate about C and the system is placed in a magnetic field B (into the plane of the ring). A circuit is now completed by connecting the ring at A and C to battery of e.m.f. V. It is found that for certain value of V, the system remains static. [Neglect resistance of the ring]
A V P C Q m 2m
9.
In static condition, find the current through rod PC a) V/R
10.
b) V/2R
c) 4V/R
d) 2V/R
Net torque applied by the tension in string on the ring can be related as: 3BVr 2 a) R
BVr 2 b) R
BVr 2 c) 3R
BVr 2 d) 2 R
passage - II In a certain region of space, there exists a uniform and constant electric field of magnitude E along the positive y-axis of a coordinate system. A charged particle of mass m and charge -q (q > 0) is projected from the origin with speed 2v at an angle of 60 with the positive x-axis in x-y
plane. When the x-coordinate of particle becomes
3mv 2 qE , a uniform and
constant magnetic field of strength B is also switched on a long positive y-axis 11.
Velocity of the particle just before the magnetic field is switched on is :
a) viˆ
3v ˆ viˆ j 2 b)
3v ˆ viˆ j 2 c)
3v ˆ 2viˆ j 2 d)
12. The magnitude of radius of curvature (just after switching on the magnetic field) of the path followed by the particle is
a) zero
b)
mv 2 mv qE qB
mv 2
c)
q E 2 +( Bv)
2
mv d) q
v2 1 + E 2 B2
Passage – III An infinitely long wire lying along z-axis carries a current I, flowing towards positive z-direction. There is no other current. Consider a circle in x-y plane with centre at (2m, 0, 0) and radius 1m. Divide the circle in r small segments and let dl denote the length of a small segment in anticlockwise direction, as shown.
13.
r r r B The path integral .dl of the total magnetic field B along the perimeter of
the given circle is, m0 I a) 8
m0 I b) 2
c) m0 I
d) 0
14.
Consider two points A(3,0,0) and B(2,1,0) on the given circle. The path B
r r
òB.dl
r
integral A of the total magnetic field B along the perimeter of the given circle from A to B is, (travelling along anticlockwise direction) m0 I 1 tan - 1 2 a) p
m0 I m0 I 1 1 tan - 1 sin - 1 2 2 b) 2p c) p MULTIPLE CORRECT CHOICE TYPE
m0 I 1 sin - 1 2 d) 2p
15. Two circular coils of radii 5cm and 10cm carry currents of 2A. The coils have 50 and 100 turns respectively and are placed in such a way that their planes as well as their centres coincide. Magnitude of magnetic field at the common centre of coils is -4 a) 8p´ 10 T if currents in the coils are in same sense
-4 b) 4p´ 10 T if currents in the coils are in opposite sense
c) zero if currents in the coils are in opposite sense -4 d) 8p´ 10 T if currents in the coils are in opposite sense
16. An infinitely long straight wire is carrying a current I 1.Adjacent to it there is another equilateral triangular wire having current I 2. Choose the wrong options a) Net force on loop is leftwards
b) Net force on loop is
rightwards c) Net force on loop is upwards downwards
I1abI2c
d) Net force on loop is
17.
A charged particle is movingr along positive y-axis in uniform electric and r ˆ
ˆ
magnetic fields E =E0 k and B =B0i . Here E0 and B0 are positive constants. Choose the correct options a) particle may be deflected towards positive z-axis b) particle may be deflected towards positive z-axis c) particle may pass undeflected d) kinetic energy of particle may remain constant 18. ABCD is a square. There is a current I in wire EFG as shown. Choose the correct options B
E
C I
F
A
G
D
a) Net magnetic field at A is into the page b) Net magnetic field at B is of zero magnitude c) Net magnetic field at C is out of the page d) Net magnetic field at D is into the page
19. There are two wires ab and cd in the same vertical plane as shown in figure. Direction of current in wire ab is rightwards. Choose the correct options
a) If wire ab is fixed then wire cd can be kept in equilibrium by the current in cd in leftward direction
b) With wire ab fixed, when in equilibrium the wire cd is in stable equilibrium c) If wire cd is fixed, then wire ab can be kept in equilibrium by flowing current in cd in rightward direction d) With wire cd fixed, when in equilibrium the wire ab is in stable equilibrium 20. A particle having a mass of 0.5 g carries a charge of 2.5 × 10 -8C. The particle is given an initial horizontal velocity of 6×10 4ms-1 in a region where is there is only a horizontal magnetic field. To keep the particle moving in a horizontal direction a) The magnetic field should be perpendicular to the direction of the velocity b) The magnetic field should be along the direction of the velocity c) Magnetic field should have a minimum value of 3.27 T d) No magnetic field is required
KEY 1- A 2 - C 3 - A 4 -A
5 - A 6 -A
7 -B
8 – B 9 -A
14-B 15-(A,C)16 - (B,C,D) 17 - (A,B,C,D)18 - (A,C,D)
10 -B 11 - A 12-C13 -D 19 - (A,C)20 - (C)
