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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 about1.5×1011m . Find the total power radiated by the sun.

Short Answer

Expert verified

a.The maximum values of the electric and magnetic fields for a sinusoidal wave with intensity1.4kW/m2 are 1026 V/m and3.42×10-6T respectively.

b. The total power radiated by the sun is 3.95×1026W.

Step by step solution

01

Define the intensity ( I ) and define the formulas.

The power transported per unit area is known as the intensity ( I ) .

The formula used to calculate the intensity( I ) is:

I=PA

Where, Ais area measured in the direction perpendicular to the energy andP is the power in watts.

The formula used to determine the amplitude of electric and magnetic fields of the wave are:

Emax=2lε0cBmax=Emaxc

Where, ε0=8.85×10-12C2/N.m2and c is the speed of light that is equal to 3.0×108m/s.

02

Determine the maximum values of electric and magnetic fields.

Given thatI=1.4kW/m2

The maximum value of electric field is:

Emax=2lε0c

Substitute the values

Emax=2×14008.85×10-123×108=1026V/m

The amplitude of magnetic field is:

Bmax=Emaxc

Substitute the values

Bmax=10263×108=3.42×10-6T

Hence, the maximum values of the electric and magnetic fields for a sinusoidal wave with intensity 1.4 kW/m2 are 1026 V/m and 3.42×10-6Trespectively.

03

Determine the power.

Given that,

I=1.4kW/m2r=1.5×1011m

The formula used to calculate the intensity ( I ) is:

I=PAP=IA

Substitute the values

P=14004π1.5×1011=1400×2.82×1023=3.95×1026W

Hence, the total power radiated by the sun is 3.95×1026W.

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