Question

Assertion (A): When a circular coil, placed in a region with its plane parallel to a magnetic field, expands radially outwards, no emf is induced in it. Reason (R): There is a constant magnetic field in the perpendicular (to the plane of the coil) direction.

• A. Both (A) and (R) are true. (R) is the correct explanation of (A).
• B. Both (A) and (R) are true. (R) is not the correct explanation of (A).
• C. (A) is true, (R) is false.
• D. (A) is false, (R) is true.

Hint:

Magnetic flux through a coil is \[ \Phi=BA\cos\theta, \] where \(\theta\) is the angle between the magnetic field and the area vector. If the magnetic field lies in the plane of the coil, then \(\theta=90^\circ\) and the flux is always zero.

Answer 1

The Correct Option is C

Step 1: Evaluate Assertion.
If the coil plane is parallel to \( \vec{B} \), the flux \( \Phi = BA\cos90^\circ = 0 \) at all times as the coil expands radially (radius changes but orientation stays parallel). Since \( \Phi \) remains 0, \( \varepsilon = -d\Phi/dt = 0 \). Assertion is TRUE.

Step 2: Evaluate Reason.
The reason says constant magnetic field in the perpendicular direction, which is incorrect — the field is parallel to the plane (perpendicular to the normal), not perpendicular to the plane. The Reason is FALSE.

\[ \boxed{\text{A is true, R is false}} \]