Moving Charges and Magnetism

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]

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].