Question

For a coil rotating in a uniform magnetic field, the phase difference between the magnetic flux linked with the coil and the current induced in it is

• A. \(90^\circ\)
• B. \(180^\circ\)
• C. \(60^\circ\)
• D. \(360^\circ\)

Hint:

If \[ \Phi=\Phi_0\cos\omega t, \] then \[ \boxed{ e=-\frac{d\Phi}{dt}\propto\sin\omega t } \] Hence, the induced current leads the magnetic flux by \[ \boxed{90^\circ.} \]

Answer 1

The Correct Option is A

Step 1: Write the expression for magnetic flux. The magnetic flux through the rotating coil is \[ \Phi=\Phi_0\cos\omega t. \]

Step 2: Find the induced current. The induced emf is \[ e=-\frac{d\Phi}{dt} =\omega\Phi_0\sin\omega t. \] Since \[ I\propto e, \] the induced current is \[ I=I_0\sin\omega t. \] Thus, the current leads the magnetic flux by \[ \boxed{90^\circ.} \] Hence, \[ \boxed{(A)} \] is the correct answer.