Question

A 210 turn flat coil of wire 25.0 cm in diameter acts as an antenna for FM radio at a frequency of 100 MHz. The Magnetic field of the incoming electromagnetic wave is perpendicular to the coil and has a maximum strength of 9.30*10^-13 T.

What power is incident on the coil?

What average emf is induced in the coil over one-fourth of a cycle?

If the radio receiver has an inductance of 2.30 microH, what capacitance must it have to resonate at 100 MHz.

Answer 1

(a)

Power incident can be found as

P = IA

where I is intensity and A is area

I = cB² / 2u_o = 3e8 * 9.3e-13² / 2 * 4e-7 = 1.0324e-10 W

A = d² / 4 = (0.25)² / 4 = 0.049087 m²

so,

P = IA

P = 5.06778e-12 W

--------------------------------------------------------------------

(b)

Emf = Nd / dt

Emf = NBA / dt

Emf = Nd²B / 4 t

we need to find emf over one - fourth of a cycle

so,

t = T / 4

Emf = Nd²B / T

also,

T = 1/f

so,

Emf = Nd²B f

Emf = 210 * * 0.25² * 9.30e-13 * 100e6

Emf = 3.835e-3 V

or

Emf = 3.835 mV

--------------------------------------------------------------------------

(c)

we can use the resonant frequency equation

Solve for C, we get

C = 1 / 4²Lf²

C = 1 / 4² * 2.30e-6 * 100e6²

C = 1.1013e-12 F

or

C = 1.1013 pF