The expression of the magnetic energy stored in a solenoid in terms of magnetic field $B$, cross-sectional area $A$ and length $l$ of the solenoid, is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $U_B=\frac{1}{2μ_0}B^2Al$
$\text{Magnetic energy stored in a solenoid: } U = \frac{1}{2} L I^2$
$\text{Inductance of solenoid: } L = \mu_0 \frac{N^2 A}{l}$
$\text{Magnetic field inside solenoid: } B = \mu_0 \frac{N}{l} I \Rightarrow I = \frac{B l}{\mu_0 N}$
$U = \frac{1}{2} \cdot \mu_0 \frac{N^2 A}{l} \cdot \left(\frac{B l}{\mu_0 N}\right)^2$
$U = \frac{1}{2} \cdot \mu_0 \frac{N^2 A}{l} \cdot \frac{B^2 l^2}{\mu_0^2 N^2}$
$U = \frac{B^2}{2 \mu_0} \cdot A \cdot l$
$\text{Answer: } U = \frac{B^2 A l}{2 \mu_0}$