2. A UHF television loop antenna has a diameter of 11 cm. The magnetic field of
ID: 2035277 • Letter: 2
Question
2. 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 (B is out of the plane) and, at one instant of time, its magnitude is changing at the rate +0.16 T/s. The magnetic field is uniform. (a) What emf is induced in the antenna? (b) What is the direction of the induced current? 3. The peak voltage of an AC source is 200 V. What is the rms voltage? 4. In an AC series circuit, the voltage in the inductor differs in phase with the voltage in the capacitor by what angle?Explanation / Answer
2A.
EMF is given by:
EMF = -N*d(phi)/dt
Magnetic flux = phi = B*A
EMF = -N*A*dB/dt
dB/dt = 0.16 T/sec
A = pi*d^2/4
Using given values:
EMF = -1*(pi*0.11^2/4)*0.16
EMF = -1.52*10^-3 V = -1.52 mV
2B.
Since magnetic field is outside the page, so induced current will be Counter-Clockwise.
3.
Vrms = Vpeak/sqrt 2
Vrms = 200/sqrt 2
Vrms = 141.4 V
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