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

Answer:

-0.00152 V

Explanation:

Parameters given:

Diameter of the loop = 11 cm = 0.11m

Rate of change of magnetic field, dB/dt = 0.16 T/s

Radius of the loop = 0.055m

The area of the loop will be:

A = pi * r²

A = 3.142 * 0.055²

A = 0.0095 m²

The EMF induced in a loop of wire due to the presence of a changing magnetic field, dB, in a time interval, dt, is given as:

EMF = - N * A * dB/dt

In this case, there's only one loop, so N = 1.

Therefore:

EMF = -1 * 0.0095 * 0.16

EMF = -0.00152 V

The negative sign indicates that the current flowing through the loop acts opposite to the change in the magnetic field.

Answer 2

Answer:

The induced emf is 0.00152 V

Explanation:

Given data:

d = 11 cm = 0.11 m

$r=\frac{d}{2} =\frac{0.11}{2} =0.055m$

The area is:

$A=\pi r^{2} =\pi *(0.055^{2} )=0.0095m^{2}$

The induced emf is:

$E=-A\frac{dB}{dt} =-(0.0095)*(0.16)=-0.00152V$

The negative indicates the direction of E.