Question

A loop antenna, such as is used on older televisions to pick up UHF broadcasts, is 25 cm in diameter. The plane of the loop is perpendicular to the oscillating magnetic field of a 170 MHz electromagnetic wave. The magnetic field through the loop is (24 nT)sin(ωt), where ω is the angular frequency of the wave. What is the maximum emf induced in the antenna?

Answer 1

Answer:

-1.25837 V

Explanation:

$B=24nTsin(\omega t)$

Time differentiated magnetic field is given by

$\dfrac{dB}{dt}=\dfrac{d24ntsin(\omega t)}{dt}\\\Rightarrow \dfrac{dB}{dt}=24nT\dfrac{dsin(\omega t)}{dt}\\\Rightarrow \dfrac{dB}{dt}=24nT\omega cos\omega t$

$cos\omega t=1$

Maximum emf is given by

$\epsilon=-A\dfrac{dB}{dt}\\\Rightarrow \epsilon=-A24nT\omega cos\omega t\\\Rightarrow \epsilon=-A24nT\omega 1\\\Rightarrow \epsilon=-\pi 0.125^2\times 24\times 10^{-9}\times 2\pi 170\times 10^{6}\\\Rightarrow \epsilon=-1.25837\ V$

The maximum emf induced in the antenna is -1.25837 V