Question

The expression for the magnetic energy stored in a solenoid in terms of magnetic field $B$, area $A$ and length $l$ of the solenoid is

• A. $\frac{B^{2} Al}{4 \mu_{0}}$
• B. $\frac{B^{2} Al}{2 \mu_{0}}$
• C. $\frac{B^{2} Al}{\mu_{0}}$
• D. $\frac{2 B^{2} A l}{\mu_{0}}$

Answer 1

Answer: (B)

$U_{B}=\frac{1}{2} L I^{2}=\frac{1}{2} L\left(\frac{B}{\mu_{0} n}\right)^{2}=\frac{1}{2}\left(\mu_{0} n^{2} A l\right)\left(\frac{B}{\mu_{0} n}\right)^{2}$
$=\frac{B^{2} A l}{2 \mu_{0}}$