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 5 mg particle carrying a charge of 5 10-6 C is moving with velocity of (3 i+2 k ) 10-2 m/s in a region having magnetic field B=0.1 k Wb/m2. It moves a distance of meter along k when it completes 5 revolutions. The value of is .

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 moving coil of galvanometer when shunted with 2 resistance gives a full scale deflection for a current of 500 mA. When a resistance of 470 is connected in series it gives a full scale deflection for 10 V potential applied on it. The value of resistance of galvanometer coil is .

The charged particle moving in a uniform magnetic field of (3 i+2 j ) T has an acceleration (4 i- x2 j ) m/s2. The value of x is .

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

A circular coil of radius 2 cm and 125 turns carries a current of 1 A. The coil is placed in a uniform magnetic field of magnitude 0.4 T. The axis of the coil makes an angle of 30° with the direction of the magnetic field. The torque acting on the coil is 10-4 N m. The value of is . ( =3.14)

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-

1 μC charge moving with velocity v= ( i-2 j+3 k ) m/s in the region of magnetic field B= (2 i+3 j-5 k ) T. The magnitude of force acting on it is 10-6 N. The value of is .

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 )

A particle of charge 1.6 and mass 16 is present in a strong magnetic field of 6.28 T. The particle is then fired perpendicular to magnetic field. The time required for the particle to return to original location for the first time is s (rounded off to the nearest integer). ( = 3.14)

A loop ABCDA, carrying current I = 12 A, is placed in a plane, consists of two semi-circular segments of radius R1 = 6 m and R2 = 4 m. The magnitude of the resultant magnetic field at center O is k 10-7 T. The value of k is . (Given 0 = 4 10-7 T m A-1) [figure]

A 4.0 cm long straight wire carrying a current of 8 A is placed perpendicular to a uniform magnetic field of strength 0.15 T. The magnetic force on the wire is mN.

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