The electric field of a plane electromagnetic wave propagating along the z-axis varies with time with an amplitude of 2 V m−12 V m-1. The average energy density of the magnetic field (in J m−3J m-3) is :Take: ε0=8.854×10−12 F
Question
The electric field of a plane electromagnetic wave propagating along the z-axis varies with time with an amplitude of 2 V m−12 V m-1. The average energy density of the magnetic field (in J m−3J m-3) is :Take: ε0=8.854×10−12 F
Solution
The energy density of an electromagnetic wave is equally divided between the electric field and the magnetic field. The total energy density (u) of an electromagnetic wave is given by the sum of the energy densities of the electric and magnetic fields.
The energy density of the electric field (uE) is given by the equation:
uE = 0.5 * ε0 * E^2
where ε0 is the permittivity of free space and E is the electric field.
Given that E = 2 V/m and ε0 = 8.854×10−12 F/m, we can substitute these values into the equation to find uE:
uE = 0.5 * 8.854×10−12 F/m * (2 V/m)^2 = 1.77 x 10^-11 J/m^3
Since the energy density is equally divided between the electric and magnetic fields, the energy density of the magnetic field (uB) is equal to the energy density of the electric field.
Therefore, uB = uE = 1.77 x 10^-11 J/m^3.
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