Question

A UHF antenna is oriented at an angle of 47o to a magnetic field that changes at a rate of 0.23 T/s. What is the induced emf of the antenna if it has a diameter of 13.4 cm? O 5.4 mV ? 2.2 ? 0027 ?

Answer 1

Answer:

Induced emf, $\epsilon=2.2\ mV$

Explanation:

It is given that,

Rate of change of magnetic field, $\dfrac{dB}{dt}=0.23\ T/s$

A UHF antenna is oriented at an angle of 47° to a magnetic field, θ = 47°

Diameter of the antenna, d = 13.4 cm

Radius, r = 6.7 m = 0.067 m

We need to find the induced emf of the antenna. It is given by :

$\epsilon=-\dfrac{d\phi}{dt}$

Where

$\phi$ = magnetic flux, $\phi=BA\ cos\theta$

So, $\epsilon=\dfrac{d(BA\ cos\theta)}{dt}$

B = magnetic field

$\epsilon=A\dfrac{d(B)}{dt}\ cos\theta$

$\epsilon=\pi r^2\times \dfrac{dB}{dt}\times cos(47)$

$\epsilon=\pi (0.067\ m)^2\times 0.23\ T-s\times cos(47)$

$\epsilon=0.0022\ V$

$\epsilon=2.2\ mV$

So, the induced emf of the antenna is 2.2 mV. Hence, this is the required solution.