Moving Charges and Magnetism

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