Moving Charges and Magnetism

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]

The magnetic field inside a 200 turns solenoid of radius 10 cm is 2.9 10-4 Tesla. If the solenoid carries a current of 0.29 A, then the length of the solenoid is cm.

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 ]

A current of 5 A exists in a square loop of side 1 2 m. Then the magnitude of the magnetic field B at the centre of the square loop will be p 10-6 T. where, value of p is [Take 0=4 10-7 T m A-1].

[figure] N equally spaced charges each of value q, are placed on a circle of radius R. The circle rotates about its axis with an angular velocity as shown in the figure. A bigger Amperian loop B encloses the whole circle where as a smaller Amperian loop A encloses a small segment. The difference between enclosed currents, IA-IB, for the given Amperian loops is

1. N22 q
2. N2 q
3. 2 Nq
4. N q

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

A long straight wire of a circular cross-section with radius 'a' carries a steady current I. The current I is uniformly distributed across this cross-section. The plot of magnitude of magnetic field B with distance r from the centre of the wire is given by

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

A tightly wound long solenoid carries a current of 1.5 A. An electron is executing uniform circular motion inside the solenoid with a time period of 75 ns. The number of turns per metre in the solenoid is . [Take mass of electron me=9 10-31 kg, charge of electron |qe|=1.6 10-19 C, 0=4 10-7 NA2, 1 ns=10-9 s]

Consider a moving coil galvanometer (MCG): Choose the correct answer from the options given below:

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