Question

In which condition EMF will be induced in loop. 
Situation-S₁: A loop is moving with uniform velocity in a uniform magnetic field perpendicular 
to its plane. 
Situation-S₂: A loop is moving with non-uniform velocity in a uniform magnetic field 
perpendicular to its plane. 
Situation-S₃: A loop is rotating about its diameter in a uniform magnetic field. 
Situation-S₄: Area of loop is changing in a uniform magnetic field. 

• A. S₂,S₃
• B. S₁,S₃
• C. S₂,S₄
• D. S₃,S₄

Answer 1

The Correct Option is D

To determine under which conditions an EMF (Electromotive Force) is induced in a loop, we must apply Faraday's Law of Electromagnetic Induction. According to the law, an EMF is induced when there is a change in magnetic flux through the loop over time. The general formula for induced EMF is:

\(\text{EMF} = - \frac{d\Phi}{dt}\)

Where:

• \(\Phi\) is the magnetic flux, given by \(\Phi = B \cdot A \cdot \cos \theta\)
• \(B\) is the magnetic field strength
• \(A\) is the area of the loop
• \(\theta\) is the angle between the magnetic field and the normal to the surface

Let's evaluate each situation:

1. Situation-\(S_1\): A loop is moving with uniform velocity in a uniform magnetic field perpendicular to its plane.
   • The magnetic flux through the loop does not change over time since both the area and the strength of the magnetic field remain constant. Therefore, no EMF is induced.
2. Situation-\(S_2\): A loop is moving with non-uniform velocity in a uniform magnetic field perpendicular to its plane.
   • Even though the movement is non-uniform, if there is no change in the magnetic flux through the loop, no EMF is induced. The velocity does not affect the flux unless the loop's orientation or area changes.
3. Situation-\(S_3\): A loop is rotating about its diameter in a uniform magnetic field.
   • As the loop rotates, the angle \(\theta\) between the plane of the loop and the magnetic field changes, thus changing the magnetic flux. This change in flux induces an EMF.
4. Situation-\(S_4\): Area of loop is changing in a uniform magnetic field.
   • The change in the area of the loop changes the magnetic flux through the loop over time, thus inducing an EMF.

Therefore, in Situation-\(S_3\) (rotation causing a change in angle) and Situation-\(S_4\) (change in area), an EMF will be induced.

Correct Answer: S₃, S₄