Moving Charges and Magnetism

A particle of charge q, mass m and kinetic energy E enters a magnetic field perpendicular to its velocity and undergoes a circular arc of radius (r). Which of the following curves represents the variation of r with E?

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

Uniform magnetic fields of different strengths (B1 and B2), both normal to the plane of the paper exist as shown in the figure. A charged particle of mass m and charge q, at the interface at an instant, moves into the region 2 with velocity v and returns to the interface. It continues to move into region 1 and finally reaches the interface. What is the displacement of the particle during this movement along the interface? [figure] (Consider the velocity of the particle to be normal to the magnetic field and B2 > B1)

1. mvqB1 (1 - B1B2 ) 2
2. mvqB1 (1 - B2B1 ) 2
3. mvqB1 (1 - B2B1 )
4. mvqB1 (1 - B1B2 )

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

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 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