The magnetic field inside a long air-cored solenoid is 0.2 T. The magnetic energy stored per unit volume inside the solenoid is nearly (take \(\mu_0=4\pi\times10^{-7}\ \mathrm{T\,m\,A^{-1}}\))
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(1.6\times10^{4}\ \mathrm{J\,m^{-3}}\)
Energy is stored in the space where a magnetic field exists. The energy per unit volume depends on the square of the field, \( u_B=B^{2}/2\mu_0 \). It does not depend on the size of the solenoid.
\( \begin{aligned} u_B &= \frac{B^{2}}{2\mu_0} \\ &= \frac{(0.2)^{2}}{2\times4\pi\times10^{-7}} \\ &= \frac{0.04}{2.51\times10^{-6}} \\ &\approx 1.6\times10^{4}\ \mathrm{J\,m^{-3}} \end{aligned} \)
NCERT (2026-27):
Example 6.9 – “(b) The magnetic energy per unit volume is,”
\( \displaystyle u_B=\frac{U_B}{V} \) “(where V is volume that contains flux)” \( \displaystyle =\frac{U_B}{Al}= \)\( \displaystyle \frac{B^{2}}{2\mu_0} \)\( \qquad (6.18) \)