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Q.

The magnetic energy stored in a long solenoid of area of cross-section A in a small region of length L is

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a

$\frac{B^{2} AL}{2 μ_{0}^{2}}$

b

$\frac{1}{2} μ_{0} B^{2} AL$

c

$\frac{AL}{2 μ_{0}}$

d

$\frac{B^{2} AL}{2 μ_{0}}$

answer is D.

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Detailed Solution

$\cup_{B} = \frac{1}{2} L_{i} i^{2}$

$B = μ_{0} ni \Rightarrow i = \frac{B}{μ_{0} n}$

$U_{B} = \frac{1}{2} L_{i} {(\frac{B}{μ_{0} n})}^{2}$

$\Rightarrow U_{B} = \frac{1}{2} (μ_{0} n^{2} AL) {(\frac{B}{μ_{0} n})}^{2} = \frac{B^{2} AL}{2 μ_{0}}$

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