ExamGOAL
Books
PreviousNext
8
MCQ (Multiple Correct Answer)

Consider a wire carrying a steady current, $I$ placed in a uniform magnetic field $\mathbf{B}$ perpendicular to its length. Consider the charges inside the wire. It is known that magnetic forces do no work. This implies that,

A
motion of charges inside the conductor is unaffected by $\mathbf{B}$, since they do not absorb energy
B
some charges inside the wire move to the surface as a result of $\mathbf{B}$
C
If the wire moves under the influence of $\mathbf{B}$, no work is done by the force
D
if the wire moves under the influence of $\mathbf{B}$, no work is done by the magnetic force on the ions, assumed fixed within the wire.
9
MCQ (Multiple Correct Answer)

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
$\oint$ B. $\mathrm{dI}=m \propto_0 I$
B
the value of $\oint \mathbf{B} \cdot \mathrm{dl}=\overline{+} 2 \alpha_0 I$ is independent of sense of $C$
C
there may be a point on $C$ where, $\mathbf{B}$ and $\mathbf{d I}$ are perpendicular
D
B vanishes everywhere on C
10
MCQ (Multiple Correct Answer)

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 $\mathbf{B}$ alone
11
MCQ (Multiple Correct Answer)

A charged particle would continue to move with a constant velocity in a region wherein,

A
$\mathbf{E}=0, \mathbf{B} \neq 0$
B
$\mathbf{E} \neq 0, \mathbf{B} \neq 0$
C
$\mathbf{E} \neq 0, \mathbf{B}=0$
D
$\mathbf{E}=0, \mathbf{B}=0$
12
Subjective

Verify that the cyclotron frequency $\omega=e B / m$ has the correct dimensions of $[T]^{-1}$.

Explanation

For a charge particle moving perpendicular to the magnetic field, the magnetic Lorentz forces provides necessary centripetal force for revolution.

$$\frac{m v^2}{R}=q v B$$

On simplifying the terms, we have

$\therefore \quad\frac{q B}{m}=\frac{v}{R}=\omega$

Finding the dimensional formula of angular frequency

$$\therefore\quad[\omega]=\left[\frac{q B}{m}\right]=\left[\frac{v}{R}\right]=[T]^{-1}$$

PreviousNext