A plane electromagnetic wave travels in a medium of relative permeability 1.6 and relative permittivity 6.44. If magnitude of magnetic intensity is 4.5 × 10–2 A m–1 at a point, what will be the approximate magnitude of electric field intensity at that point? (Given: permeability of free space μ0 = 4π × 10−7NA−2, speed of light in vacuum c = 3 × 108 m/s)
Question
A plane electromagnetic wave travels in a medium of relative permeability 1.6 and relative permittivity 6.44. If magnitude of magnetic intensity is 4.5 × 10–2 A m–1 at a point, what will be the approximate magnitude of electric field intensity at that point? (Given: permeability of free space μ0 = 4π × 10−7NA−2, speed of light in vacuum c = 3 × 108 m/s)
Solution
To find the approximate magnitude of the electric field intensity at a point, we can use the relationship between the magnetic field intensity (H) and the electric field intensity (E) in an electromagnetic wave.
The relationship is given by:
E = c * H / sqrt(μ0 * ε0)
where: E is the electric field intensity, c is the speed of light in vacuum, H is the magnetic field intensity, μ0 is the permeability of free space, and ε0 is the permittivity of free space.
Given that the magnitude of the magnetic field intensity (H) is 4.5 × 10^(-2) A m^(-1), we can substitute the values into the equation to find the electric field intensity (E).
Using the given values: c = 3 × 10^8 m/s (speed of light in vacuum) μ0 = 4π × 10^(-7) N A^(-2) (permeability of free space)
Substituting the values into the equation:
E = (3 × 10^8 m/s) * (4.5 × 10^(-2) A m^(-1)) / sqrt(4π × 10^(-7) N A^(-2) * 6.44)
Calculating the expression:
E ≈ 1.32 × 10^(-6) N/C
Therefore, the approximate magnitude of the electric field intensity at the given point is approximately 1.32 × 10^(-6) N/C.
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