Question

When a wire loop is rotated in a magnetic field, the direction of induced e.m.f. changes once in each
\[
  A.{\text{ }}\dfrac{1}{4}{\text{ revolution}} \\
  B.{\text{ }}\dfrac{1}{2}{\text{ revolution}} \\
  C.{\text{ }}1{\text{ revolution}} \\
  D.{\text{ }}2{\text{ revolution}} \\
 \]

Answer 1

Hint: In order to solve the problem first use the formula for the flux of the magnetic field through the loop and then in order to find the correct option use the different angles for finding the revolution.
Formula used- $\phi = B.A\cos \omega t,{\text{Emf}} = - \dfrac{{d\phi }}{{dt}}$

Complete Step-by-Step solution:
As we know that:
Flux of the magnetic field through the loop is given by:
$\phi = B.A\cos \omega t$
Also we know that e.m.f. is given by:
$
  {\text{Emf}} = - \dfrac{{d\phi }}{{dt}} \\
   \Rightarrow {\text{Emf}} = - \dfrac{{d\left( {B.A\cos \omega t} \right)}}{{dt}} \\
   \Rightarrow {\text{Emf}} = B.A\sin \omega t \\
 $
Now let us find the e.m.f. for different angles in order to find the revolution.
For the given angles
 \[
  \omega t = 0{\text{ to }}\pi \\
  \sin \omega t = + ve \\
 \]
And for the given angles
 \[
  \omega t = \pi {\text{ to 2}}\pi \\
  \sin \omega t = - ve \\
 \]
So after the change of $\pi $ angle, the direction of induced e.m.f. changes. Also we know that $\pi $ angle represents half revolution.
Hence, after the change of half revolution the direction of induced e.m.f. changes.
So, the correct answer is option B.

Note- A magnetic field is a vector field that defines the magnetic effect in relative motion of electrical charges and magnetic materials. At any point of a current bearing circular ring the magnetic field lines are concentric circles. The magnetic field position of each part of the rotating loop can be determined by using the rule of thumb on the right side. The magnetic field lines are parallel, at the middle of the revolving circle.