Question

A UHF television loop antenna has a diameter of 11 cm. The magnetic field of a TV signal is normal to the plane

Answer 1

Hi there,

I think your question was incomplete. I am hoping that the following question, is the complete required question:

A UHF television loop antenna has a diameter of 11 cm. The magnetic field of a TV signal is normal to the plane of the loop and at one instant of time. Its magnitude is changing at the rate 0.16 T/s. The magnetic field is uniform. What emf is induced in the antenna?

Answer: 1.52 * 10⁻³ V

Explanation:

The radius of the loop, r = d/2 = 11/2 = 5.5 cm = 0.055 m

The magnitude of changing magnetic field, dB/dt = 0.16 T/s

In the question above we are given that, the magnetic field is normal to the plane of the loop and uniform at any instant of time.

∴ The magnetic flux through the loop,  

∅ = (area of the loop) * (magnetic field over the loop) = πr² * B …… (i)

Now, by using Faraday’s Law,  

The magnitude of the emf induced in the antennae,

e = d∅ / dt

⇒ e = d[πr² * B] / dt

⇒ e = πr² * dB/dt

substituting the values, we get

⇒ e = 3.14 * (0.055)² * 0.16 = 0.001519 = 1.52 * 10⁻³ V