Moving Charges and Magnetism

A current carrying circular loop of radius 2 cm with unit normal n= k+ i 2 is placed in a magnetic field, B=B0 (3 i+2 k ). If B0=4 10-3 T and current I=100 2 A, the torque experienced by the loop is Wb.A. ( =3.14)

1. 16 10-5 k
2. 5024 10-7 k
3. 5024 10-7 i
4. 5024 10-7 j

A small cube of side 1 mm is placed at the centre of a circular loop of radius 10 cm carrying a current of 2 A. The magnetic energy stored inside the cube is 10-14 J. The value of is . ( 0=4 10-7 Tm/A, =3.14)

1. 6.28
2. 6.28 10-6
3. 628
4. 6.28 10-4

A current of 30 A each flows in opposite directions in two conducting wires, placed parallel to each other at a distance of 8 cm. The magnetic field at the mid point between the two wires is μT. ( 04 =10-7 N/A2)

1. 30
2. 300
3. 150
4. 0.0

A particle of charge q and mass m is projected from origin with an initial velocity v= ( v0 2 x+ v0 2 y ). There exists a uniform magnetic field B=B0 z and a space varying electric field E=E0e- x x within the region 0 x L. After travelling a distance such that x-coordinate has changed from x=0 to x=L, the change in the kinetic energy is .

1. qE0 [1-e- L ]
2. ( v0qB02 ) [2-e-2 L ]
3. qE0 [1+e- L ]
4. q ( E0+v0B0 ) [1-e- L/2 ]

A voltmeter with internal resistance of x Ω can be used to measure up to 20 V. In order to increase its measuring range to 30 V, the required modification is to .

1. connect resistor of x2 Ω, in series with voltmeter.
2. connect resistor of x2 Ω, in parallel to voltmeter.
3. connect a resistor of x Ω in series with voltmeter.
4. connect resistor of 2x Ω in parallel to voltmeter.

An insulated wire is wound so that it forms a flat coil with N=200 turns. The radius of the innermost turn is r1=3 cm, and of the outermost turn r2=6 cm. If 20 mA current flows in it then the magnetic moment will be 10-2 A m2. The value of is .

1. 4.4
2. 2.64
3. 3.25
4. 1.2

Two identical long current carrying wires are bent into the shapes shown in the following figures. If the magnitude of magnetic fields at the centres P and Q of a semicircular arc are B1 and B2 respectively, then the ratio B1B2 is . [figure]

1. 2+ 1+
2. 1+ 1-
3. 2+ 1-
4. 1+ 2-

A particle having charge 10-9 C moving in x-y plane in fields of 0.4 j N/C and 4 10-3 k T experiences a force of (4 i+2 j ) 10-10 N. The velocity of the particle at that instant is m/s.

1. 50 i+100 j
2. 100 i+50 j
3. -50 i+100 j
4. 50 i-100 j

The magnetic field at the centre of a current carrying circular loop of radius R is 16 . The magnetic field at a distance x = 3R on its axis from the centre is .

1. 8
2. 2
3. 4
4. 2 2

Three long straight wires carrying current are arranged mutually parallel as shown in the figure. The force experienced by 15 cm length of wire Q is . ( 0 = 4 10-7 T m/A) [figure]

1. 6 10-6 N towards P
2. 6 10-6 N towards R
3. 6 10-7 N towards P
4. 6 10-7 N towards R

A long cylindrical conductor with large cross section carries an electric current distributed uniformly over its cross-section. Magnetic field due to this current is: Choose the correct answer from the options given below:

1. B, C Only
2. E Only
3. A, D Only
4. D Only

A moving coil galvanometer of resistance 100 shows a full scale deflection for a current of 1 mA. The value of resistance required to convert this galvanometer into an ammeter, showing full scale deflection for a current of 5 mA, is

1. 25
2. 2.5
3. 0.5
4. 10

Two identical circular loops P and Q each of radius r are lying in parallel planes such that they have common axis. The currents through P and Q are I and 4I respectively in clockwise direction as seen from O. The net magnetic field at O is : [figure]

1. 0 I4 2r towards Q
2. 3 0 I4 2r towards Q
3. 3 0 I4 2r towards P
4. 0 I4 2r towards P

The current passing through a conducting loop in the form of equilateral triangle of side 4 3 cm is 2 A. The magnetic field at its centroid is 10-5 T. The value of is . (Given: 0 = 4 10-7 SI units)

1. 3 3
2. 2 3
3. 3
4. 32

A current carrying solenoid is placed vertically and a particle of mass m with charge Q is released from rest. The particle moves along the axis of solenoid. If g is acceleration due to gravity then the acceleration (a) of the charged particle will satisfy :

1. a > g
2. a = 0
3. 0 < a < g
4. a = g

An infinitely long straight wire carrying current I is bent in a planar shape as shown in the diagram. The radius of the circular part is r. The magnetic field at the centre O of the circular loop is : [figure]

1. - 02 Ir( + 1) i
2. - 02 Ir( - 1) i
3. 02 Ir( + 1) i
4. 02 Ir( - 1) i

Figure shows a current carrying square loop ABCD of edge length 'a' lying in a plane. If the resistance of the ABC part is r and that of ADC part is 2r, then the magnitude of the resultant magnetic field at centre of the square loop is [figure]

1. 2 0 I3 a
2. 2 0 I3 a
3. 3 0 I 2a
4. 0 I2 a

A particle of charge q, mass m and kinetic energy E enters a magnetic field perpendicular to its velocity and undergoes a circular arc of radius (r). Which of the following curves represents the variation of r with E?

1. [figure]
2. [figure]
3. [figure]
4. [figure]

Uniform magnetic fields of different strengths (B1 and B2), both normal to the plane of the paper exist as shown in the figure. A charged particle of mass m and charge q, at the interface at an instant, moves into the region 2 with velocity v and returns to the interface. It continues to move into region 1 and finally reaches the interface. What is the displacement of the particle during this movement along the interface? [figure] (Consider the velocity of the particle to be normal to the magnetic field and B2 > B1)

1. mvqB1 (1 - B1B2 ) 2
2. mvqB1 (1 - B2B1 ) 2
3. mvqB1 (1 - B2B1 )
4. mvqB1 (1 - B1B2 )

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. In the light of the above statements, choose the correct answer from the options given below

1. Both A and R are true but R is NOT the correct explanation of A
2. A is false but R is true
3. A is true but R is false
4. Both A and R are true and R is the correct explanation of A

A monochromatic light of wavelength is incident on a metallic plate having work function . An electron, emitted normally to the plate from a point A with maximum kinetic energy, enters a constant magnetic field, perpendicular to the initial velocity of electron. The electron passes through a curve and hits back the plate at a point B. The distance between A and B is : (Given : The magnitude of charge of an electron is e and mass is m, h is Planck's constant and c is velocity of light. Take the magnetic field exists throughout the path of electron)

1. 2m ( hc - )/eB
2. 8 m ( hc - )/eB
3. m(hc/ - )/eB
4. 2 m(hc/ - )/eB

Let B1 be the magnitude of magnetic field at center of a circular coil of radius R carrying current I. Let B2 be the magnitude of magnetic field at an axial distance 'x' from the center. For x : R = 3 : 4, B2B1 is :

1. 64 : 125
2. 25 : 16
3. 4 : 5
4. 16 : 25

In a moving coil galvanometer, two moving coils M1 and M2 have the following particulars : R1 = 5 , N1 = 15, A1 = 3.6 10-3 m2, B1 = 0.25 T R2 = 7 , N2 = 21, A2 = 1.8 10-3 m2, B2 = 0.50 T Assuming that torsional constant of the springs are same for both coils, what will be the ratio of voltage sensitivity of M1 and M2 ?

1. 1 : 1
2. 1 : 3
3. 1 : 2
4. 1 : 4

An electron with mass 'm' with an initial velocity (t = 0) v = v0 i (v0 > 0) enters a magnetic field B = B0 j. If the initial de Broglie wavelength at t = 0 is 0 then its value after time 't' would be :

1. 0 1 - e2 B02 t2m2
2. 0
3. 0 1 + e2 B02 t2m2
4. 0 1 + e2 B02 t2m2

Consider a long straight wire of a circular cross-section (radius a) carrying a steady current I. The current is uniformly distributed across this cross-section. The distances from the centre of the wire’s cross-section at which the magnetic field [inside the wire, outside the wire] is half of the maximum possible magnetic field, any where due to the wire, will be :

1. [a/2, 3a]
2. [a/4, 3a/2]
3. [a/2, 2a]
4. [a/4, 2a]

Consider a long thin conducting wire carrying a uniform current I. A particle having mass "m" and charge "q" is released at a distance "a" from the wire with a speed v0 along the direction of current in the wire. The particle gets attracted to the wire due to magnetic force. The particle turns round when it is at distance x from the wire. The value of x is [ 0 is vacuum permeability]

1. a [1 - mv02q 0 I ]
2. ae- 4 m v0q 0 I
3. a [1 - mv0q 0 I ]
4. a2

[figure] An infinite wire has a circular bend of radius a, and carrying a current I as shown in the figure. The magnitude of magnetic field at the origin O of the arc is given by:

1. 02 Ia [ 2+2 ]
2. 04 Ia [ 3 2+1 ]
3. 04 Ia [ 2+1 ]
4. 04 Ia [ 3 2+2 ]