Moving Charges and Magnetism

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]

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

A galvanometer having a coil of resistance 30 need 20 mA of current for full-scale deflection. If a maximum current of 3 A is to be measured using this galvanometer, the resistance of the shunt to be added to the galvanometer should be 30X , where X is

1. 447
2. 298
3. 149
4. 596

An electron projected perpendicular to a uniform magnetic field B moves in a circle. If Bohr's quantization is applicable, then the radius of the electronic orbit in the first excited state is :

1. h eB
2. 4h eB
3. h2 eB
4. 2h eB

A proton is moving undeflected in a region of crossed electric and magnetic fields at a constant speed of 2 105 m s-1. When the electric field is switched off, the proton moves along a circular path of radius 2 cm . The magnitude of electric field is x 104 N/C. The value of x is . Take the mass of the proton =1.6 10-27 kg.

Two long parallel wires X and Y, separated by a distance of 6 cm , carry currents of 5 A and 4A, respectively, in opposite directions as shown in the figure. Magnitude of the resultant magnetic field at point P at a distance of 4 cm from wire Y is x 10-5 T. The value of x is . Take permeability of free space as 0=4 10-7 SI units. [figure]