In an electromagnetic wave, the ratio of energy densities of electric and magnetic fields is ____________.
Fill in the blank with the correct answer from the options given below.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( 1 : 1 \)
The energy densities of the electric and magnetic fields are
\( \displaystyle u_E = \frac{1}{2}\varepsilon_0 E^{2}, \qquad u_B = \frac{B^{2}}{2\mu_0} \)
In an electromagnetic wave \( E = cB \) and \( c^{2} = 1/(\mu_0\varepsilon_0) \):
\( \displaystyle u_E = \frac{1}{2}\varepsilon_0 c^{2} B^{2} = \frac{1}{2}\varepsilon_0 \cdot \frac{1}{\mu_0 \varepsilon_0} B^{2} = \frac{B^{2}}{2\mu_0} = u_B \)
So the energy is shared equally between the two fields, and the ratio is \( 1 : 1 \).
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