Question

A conducting loop rotates with constant angular velocity about its fixed diameter in a uniform magnetic field, whose direction is perpendicular to that fixed diameter

• A. The emf will be maximum at the moment when flux is zero
• B. The emf will be $0$ at the moment when flux is maximum
• C. The emf will be maximum at the moment when plane of the loop is parallel to the magnetic field
• D. The phase difference between the flux and the emf is $\pi /2$
• E. answer required

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A The emf will be maximum at the moment when flux is zero
B The emf will be $0$ at the moment when flux is maximum
C The phase difference between the flux and the emf is $\pi /2$
D The emf will be maximum at the moment when plane of the loop is parallel to the magnetic field

Let the angle that area vector of the loop makes with the magnetic field be $\theta$ at some arbitrary point of time.

Then, flux through the loop $=\overrightarrow{B}.\overrightarrow{A}=BA\cos \theta$

Thus, emf produced $=-\frac{d\varphi }{dt}=BA\sin \theta \frac{d\theta }{dt}=BA\omega \sin \theta$

Emf is maximum for $\theta ={90}^{\circ }$ while flux is zero at that orientation.

Similarly, the emf will be0 at the moment when flux is maximum.

Emf is maximum for $\theta ={90}^{\circ }$ , that is when plane of the loop is parallel to the magnetic field.

Phase difference between sin and cos function is $\pi /2.$