Question

The energy flow to the earth from sunlight is about 2 1.4 kW>m . (a) Find the maximum values of the electric and mag- netic fields for a sinusoidal wave of this intensity. (b) The distance from the earth to the sun is about 1.5 * 1011 m. Find the total power radiated by the sun.

Answer 1

Complete question is;

The energy flow to the earth from sunlight is about 1.4kW/m²

(a) Find the maximum values of the electric and magnetic fields for a sinusoidal wave of this intensity.

(b) The distance from the earth to the sun is about 1.5 × 10^(11) m. Find the total power radiated by the sun.

Answer:

A) E_max ≈ 1026 V/m

B_max = 3.46 × 10^(-6) T

B) P = 3.95 × 10^(26) W

Explanation:

We are given;

Intensity; I = 1.4kW/m² = 1400 W/m²

Formula for maximum value of electric field in relation to intensity is given as;

E_max = √(2I/(ε_o•c))

Where;

ε_o is electric constant = 8.85 × 10^(-12) C²/N.m²

c is speed of light = 3 × 10^(8) m/s

Thus;

E_max = √(2 × 1400)/(8.85 × 10^(-12) × 3 × 10^(8)))

E_max ≈ 1026 V/m

Formula for maximum magnetic field is;

B_max = E_max/c

B_max = 1026/(3 × 10^(8))

B_max = 3.46 × 10^(-6) T

Formula for the total power is;

P = IA

Where;

A is area = 4πr²

We are given;

Radius; r = 1.5 × 10^(11) m

A = 4π × (1.5 × 10^(11))² = 2.82 × 10^(23) m²

P = 1400 × 2.82 × 10^(23)

P = 3.95 × 10^(26) W