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. $\frac{2B^{2}Al}{{\mu }_0}$

Answer 1

Answer: (B)

$U_B=\frac{1}{2}L{I}^2=\frac{1}{2}L{\left(\frac{B}{{\mu }_{0}n}\right)}^2=\frac{1}{2}\left({\mu }_0{n}^{2}Al\right){\left(\frac{B}{{\mu }_{0}n}\right)}^2$
$=\frac{B^{2}Al}{2{\mu }_0}$