Question

Monochromatic electromagnetic radiation illuminates an area of a surface. The electric and magnetic fields of the waves are then doubled in magnitude. How is the total energy incident on the surface per unit time affected by this increase in the electric and magnetic fields?
a) The total energy is not affected by this change.
b) The total energy will increase by a factor of two.
c) The total energy will increase by a factor of four.
d) The total energy will decrease by a factor of two.
e) The total energy will decrease by a factor of four.

Answer 1

Answer:

c) True. factor four

Explanation:

The energy density of an electromagnetic wave is given by

             u = ½ ε₀ E² = B² / 2μ₀

Where ε₀ is the dielectric constant and μ₀ the magnetic permittivity.

Let's apply this equation to the present case

 

If we double the electro field

               E ’= 2 E₀

               u’= ½  ε₀ (2E₀)²

               u’= ½ ε₀ Eo² 4

               u’= 4 u₀

Therefore the energy is multiplied by four

Let's check the answers

a) False

b) False

c) True

d) False

e) False

Answer 2

In the electric and magnetic field:

c) The total energy will increase by a factor of four.

Energy density:

The energy density of an electromagnetic wave is given by

u = ½ ε₀ E² = B² / 2μ₀

Where,

ε₀ is the dielectric constant and

μ₀ the magnetic permittivity.

For our given conditions: If we double the electric field E’= 2 E₀

u’= ½ ε₀ (2E₀)²

u’= ½ ε₀

Eo² 4u’= 4 u₀

Thus, correct option is C.

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