Moving Charges and Magnetism

A 5 mg particle carrying a charge of 5 10-6 C is moving with velocity of (3 i+2 k ) 10-2 m/s in a region having magnetic field B=0.1 k Wb/m2. It moves a distance of meter along k when it completes 5 revolutions. The value of is .

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 )

A particle of charge 1.6 and mass 16 is present in a strong magnetic field of 6.28 T. The particle is then fired perpendicular to magnetic field. The time required for the particle to return to original location for the first time is s (rounded off to the nearest integer). ( = 3.14)

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