A 200-turn flat coil of wire 30.0 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 1.00×10−12 T.

(a) What power is incident on the coil?
(b) What average emf is induced in the coil over one-fourth of a cycle?
(c) If the radio receiver has an inductance of 2.50 μH, what capacitance must it have to resonate at 100 MHz?

a)P = 8.43 × 10⁻¹² W

b) e =5.65 × 10⁻³ V

c) c = 1.01 × 10⁻¹² F

Explanation:

(a) What power is incident on the coil?

diameter(d) = 30.0 cm = 30 × 10⁻² m

Magnetic strength(B₀) = 1 × 10⁻¹² T

Speed of light(c) = 3 × 10⁸ m/s

Permeability of vacuum(u₀) = 4π × 10⁻⁷ N/A² = 12.57 × 10⁻⁷ N/A²

The magnetic field intensity(I) is given as:

The power incident on the coil(P) is given as:

Where A is the coil area = πd²/4 = 3.14d²/4

Therefore,

substituting values,

P = 8.43 × 10⁻¹² W

(b) What average emf is induced in the coil over one-fourth of a cycle

Frequency (f) = 100 MHz = 100 × 10⁶ Hz

emf(e) = ?

Number of turns(N) = 200 turns

Time(T) = 1/f = 1/(100 × 10⁶) = 10⁻⁸ s

dt =

From Faraday's law of electromagnetism:

e =5.65 × 10⁻³ V

c) If the radio receiver has an inductance of 2.50 μH, what capacitance must it have to resonate at 100 MHz?

Capacitance(c) = ?

Inductance(L) = 2.5 μH = 2.5 × 10⁻⁶ H

resonant frequency(f₀) = 100 MHz = 100 × 10⁶ Hz

At resonant frequency, the capacitance impedance and inductive impedance are equal. Therefore:

c = 1.01 × 10⁻¹² F

probably not the "magnets"in the magnet, so to speak, are thought to be electrons orbiting in shells. vurrent loops two sides to the loop

the area between the graph and the t axis