Moving Charges and Magnetism · Question 31

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]

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 ]