(8%) Problem 3: An antenna with power P = 3.8 x 10^3 W is radiating spherical el

Question

(8%) Problem 3: An antenna with power P = 3.8 x 10^3 W is radiating spherical electromagnetic waves. Consider a place which is d = 235 m away from the antenna. Randomized Variables P=3.8x 10^3W d = 235 m Part (a) Express the average intensity of the wave, I, in terms of P and d. 25% Part (b) Express I in terms of the electric field magnitude E max, the speed of light c, and the permeability of free space . 25% Part(c) Find E max in terms of p,d,c, and mu 0. 25% Part (d) Solve for the numerical value of E max in volts per meter.

Explanation / Answer

Here ,

Power , P = 3.8 *10^3 W

d = 235 m

a) intensity is given as I = Power/area

I = P/(4*pi*d^2)

the intensity of the wave is P/(4*pi*d^2)

b)

as Intensity is given as,

I = 0.5 * Emax^2/(c*u0)

c)

Now,

P/(4*pi*d^2) = 0.5 * Emax^2/(c*u0)

Emax = sqrt(2P*c*u0/(4*pi*d^2))

the Emax is given as sqrt(2P*c*u0/(4*pi*d^2))

d)

Emax = sqrt(2 * 3800 * 3 *10^8 * 4pi *10^-7 /(4 *pi*235^2))

Emax = 2.03 V/m

the maximum electric field is 2.03 V/m

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