Question

A coil of area \( A \) and \( N \) turns is rotating with angular velocity \( \omega \) in a uniform magnetic field \( B \) about an axis perpendicular to \( B \). Magnetic flux \( \phi \) and induced emf \( \varepsilon \) across it, at an instant when \( B \) is parallel to the plane of the coil, are:

• A. \( \phi = AB, \varepsilon = 0 \)
• B. \( \phi = 0, \varepsilon = 0 \)
• C. \( \phi = 0, \varepsilon = NAB\omega \)
• D. \( \phi = AB, \varepsilon = NAB\omega \)

Hint:

When a coil rotates in a magnetic field, the flux and induced emf depend on the orientation of the magnetic field and the angular velocity of rotation.

Answer 1

The Correct Option is D

The magnetic flux \( \phi \) is given by: \[ \phi = B \cdot A = AB \] At the instant when \( B \) is parallel to the plane of the coil, the induced emf \( \varepsilon \) is given by: \[ \varepsilon = -N \frac{d\phi}{dt} \] Since \( \phi = AB \), and the coil is rotating with angular velocity \( \omega \), we have: \[ \varepsilon = -N \frac{d(AB)}{dt} = -N \cdot A \cdot B \cdot \omega = NAB\omega \]