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Chapter 17: Problem 18

In an electromagnetic wave the average energy density associated with magnetic field will be (A) \(\frac{1}{2} L I^{2}\) (B) \(\frac{B^{2}}{2 \mu_{0}}\) (C) \(\frac{1}{2} \mu_{0} B^{2}\) (D) \(\frac{1}{2} \frac{q}{B^{2}}\)

Short Answer

Expert verified
The correct expression for the average energy density associated with the magnetic field in an electromagnetic wave is given by option (B): Average Energy Density \(= \frac{B^2}{2 \mu_{0}}\).

Step by step solution

01

1. Determine the magnetic field energy density formula

The average energy density associated with the magnetic field of an electromagnetic wave can be defined using the magnetic field intensity (B) and the magnetic permeability constant (渭鈧�), as given by the following formula: Average Energy Density \(= \frac{1}{2} \cdot \frac{B^2}{\mu_{0}}\) Now, we will compare this formula with the given options.
02

2. Compare the discovered formula with the given options

We look for the option that matches the formula we found: (A) \(\frac{1}{2} L I^{2}\) - This expression is associated with the energy stored in an inductor, not in an electromagnetic wave's magnetic field. (B) \(\frac{B^{2}}{2 \mu_{0}}\) - This expression matches our formula, as it represents the average energy density in the magnetic field of an electromagnetic wave. (C) \(\frac{1}{2} \mu_{0} B^{2}\) - This expression has an extra 渭鈧� factor in the numerator, which makes it incorrect. (D) \(\frac{1}{2} \frac{q}{B^{2}}\) - This expression does not correspond to the average energy density associated with the magnetic field of an electromagnetic wave.
03

3. Determine the correct answer

According to our analysis, the correct expression for the average energy density associated with the magnetic field in an electromagnetic wave is given by option (B): Average Energy Density \(= \frac{B^2}{2 \mu_{0}}\)

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