Radiation from the Sun reaches the Earth at a rate of 1.40 kW / m^2 above the atmosphere and at

Radiation from the Sun reaches the Earth at a rate of 1.40...

Radiation from the Sun reaches the Earth at a rate of $1.40 \mathrm{~kW} / \mathrm{m}^{2}$ above the atmosphere and at a rate of $1.00 \mathrm{~kW} / \mathrm{m}^{2}$ on an ocean beach. a) Calculate the maximum values of $E$ and $B$ above the atmosphere. b) Find the pressure and the force exerted by the radiation on a person lying flat on the beach who has an area of $0.750 \mathrm{~m}^{2}$ exposed to the Sun.

Radiation from the Sun reaches the Earth at a rate of $1.40 \mathrm{~kW} / \mathrm{m}^{2}$ above the atmosphere and at a rate of $1.00 \mathrm{~kW} / \mathrm{m}^{2}$ on an ocean beach.
a) Calculate the maximum values of $E$ and $B$ above the atmosphere.
b) Find the pressure and the force exerted by the radiation on a person lying flat on the beach who has an area of $0.750 \mathrm{~m}^{2}$ exposed to the Sun.

Key Concepts

Force Due to Radiation

The force exerted by radiation on an object is found by multiplying the radiation pressure by the area over which the radiation is incident. This provides a way to quantify the mechanical effect of electromagnetic radiation on matter. The concept is crucial in applications where light-induced forces are significant, linking the pressure of electromagnetic waves to observable force effects on physical objects.

Radiation Pressure

Radiation pressure is the pressure exerted by electromagnetic radiation upon any surface due to the momentum carried by the photons. It can be calculated from the intensity of the radiation, with the basic relation for a perfectly absorbing surface being p = I/c, where I is the intensity and c is the speed of light. This concept is important for understanding how light can exert mechanical forces on objects.

Electromagnetic Waves

Electromagnetic waves consist of oscillating electric and magnetic fields that propagate through space and time. Their behavior and properties are described by Maxwell's equations, and one key relation between the fields is that the magnitude of the electric field (E) is equal to the speed of light (c) multiplied by the magnitude of the magnetic field (B), i.e., E = cB. This relationship is fundamental to understanding how energy is transmitted through these waves.

Intensity of Electromagnetic Radiation

The intensity of an electromagnetic wave is defined as the power per unit area carried by the wave. It is directly related to the squared amplitudes of the fields. For instance, the average intensity can be expressed in terms of the electric field as I = 1/2 ?? c E², where ?? is the permittivity of free space. This concept links the measurable power transfer of the wave to the microscopic properties of the fields themselves.

Field Amplitudes

Field amplitudes refer to the maximum or peak values of the electric and magnetic fields in an electromagnetic wave. These amplitudes are crucial because they determine the energy density of the wave. Using the formula for intensity, one can calculate the amplitude of the electric field and subsequently use the relation E = cB to determine the corresponding magnetic field amplitude, thereby obtaining a complete picture of the wave's characteristics.

Transcript

00:01 We have radiation from the sun, which is at the earth at the rate i equals to 1 .40 kilowatt per meter square.

00:08 And we have another radiation at the rate i dash equals to 1 .00 kilowatt per meter square on the ocean beach.

00:18 So for the part a of the question, we have to calculate the maximum value of e and b above the atmosphere.

00:25 So intensity i it is given by i equals to 1 by c multiplied by mu not multiplied by erms square okay so from here we get intensity erms equals to under root of i multiplied by c multiplied by mu not okay so substituting values so we get erms is to under root of i which is 1 .40 multiplied by 10 to the power 3 watt per meter square multiplied by 3 into 10 to the power 8 meter per second multiplied by mu not which is 4 pi multiplied by 10 to the power minus 7 henry per meter or tesla meter per ampere.

01:08 So from here after solving we get erms equals to 7 to 6 .49 volt per meter.

01:16 Okay.

01:16 So now we can calculate the maximum value.

01:19 So, e, this will be equals to under root 2 times of rms.

01:24 So we get under root 2 multiplied by erms is 726 .49 volt per meter.

01:30 So from here we get maximum value for the electric field, e equals to 1027 .4 volts per meter.

01:39 Okay, so this become the answer for the maximum value of electric field.

01:42 Now, calculating the maximum value for the magnetic field and it will be given by b equals to e by c...