The energy density in magnetic field B is proportional to

Options

A. `1/B`
B. `1/(B^(2))`
C. B
D. `B^(2)`

Answer

To determine the energy density in a magnetic field \( B \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand Energy Density**:
Energy density (\( u \)) is defined as the energy per unit volume. In the context of a magnetic field, it can be expressed in terms of the magnetic field \( B \).

2. **Recall the Formula for Energy Density in a Magnetic Field**:
The energy density in a magnetic field is given by the formula:
\[ u = \frac{B^2}{2\mu_0} \]
where \( \mu_0 \) is the permeability of free space.

3. **Identify Proportionality**:
From the formula \( u = \frac{B^2}{2\mu_0} \), we can see that the energy density \( u \) is proportional to the square of the magnetic field \( B \).

4. **Conclusion**:
Therefore, we conclude that the energy density in a magnetic field \( B \) is proportional to \( B^2 \).

### Final Answer:
The energy density in a magnetic field \( B \) is proportional to \( B^2 \).

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