Moving Charges and Magnetism

Verify that the cyclotron frequency ω = eB/m has the correct dimensions of [T]^-1

A charged particle would continue to move with a constant velocity in a region wherein,
(a) E = 0,B≠0 (b) E≠0,B≠0
(c) E≠0,B = 0 (d) E = 0, B = 0

A cubical region of space is filled with some uniform electric and magnetic fields. An electron enters the cube across one of its faces with velocity v and a positron enters via opposite face with velocity -v. At this instant,
(a) The electric forces on both the particles cause identical accelerations.
(b) The magnetic forces on both the particles cause equal accelerations.
(c) Both particles gain or loose energy at the same rate.
(d) The motion of the Centre of Mass (CM) is determined by B alone.

Two identical current carrying coaxial loops, carry current I in an opposite sense. A simple amperian loop passes through both of them once. Calling the loop as C,
(a) ?Bdl =m $\propto$ I
(b) the value of  ?B.dl = ±2 $\propto$ I is independent of sense of C
(c) there may be a point on C where, B and dl are perpendicular
(d) B vanishes everywhere on C

Consider a wire carrying a steady current, I placed in a uniform magnetic field B perpendicular to its length. Consider the charges inside the wire. It is known that magnetic forces do not work. This implies that,
(a) motion of charges inside the conductor is unaffected by B, since they do not absorb energy.

(b) Some charges inside the wire move to the surface as a result of B.
(c) If the wire moves under the influence of B, no work is done by the force.
(d) If the wire moves under the influence of B, no work is done by the magnetic force on the ions, assumed fixed within the wire.

The gyro-magnetic ratio of an electron in an H-atom, according to Bohr model, is .
(a) Independent of which orbit it is in.
(b) Negative
(c) Positive
(d) Increases with the quantum number n.

A circular current loop of magnetic moment M is in an arbitrary orientation in an external magnetic field B. The work done to rotate the loop by 30° about an axis perpendicular to its plane is

(a) MB (b) $\frac{\sqrt[]{3}}{2}\mathit{M}\mathit{B}$ (c) MB/2 (d) zero

In a cyclotron, a charged particle
(a) Undergoes acceleration all the time
(b) Speeds up between the dees because of the magnetic field
(c) Speeds up in a dee
(d) Slows down within a dee and speeds up between dees

An electron is projected with uniform velocity along the axis of a current carrying long solenoid. Which of the following is true?
(a) The electron will be accelerated along the axis
(b) The electron path will be circular about the axis
(c) The electron will experience a force at 45° to the axis and hence execute a helical path
(d) The electron will continue to move with uniform velocity along the axis of the solenoid

A current carrying circular loop of radius R is placed in the x-y plane with centre at the origin. Half of the loop with x >0 is now bent so that it now lies in the y-z plane.
(a) The magnitude of magnetic moment now diminishes.
(b) The magnetic moment does not change.
(c) The magnitude of B at (0,0, z), z>>R increases.
(d) The magnitude of B at (0,0,z), z>>R is unchanged.