Question

Magnetic energy per unit volume is represented by
$A.\dfrac{{{B}^{2}}}{2{{\mu }_{0}}}$
$B.\dfrac{{{B}^{2}}}{2\mu _{0}^{2}}$
$C.\dfrac{2{{B}^{2}}}{{{\mu }_{0}}}$
$D.\dfrac{{{B}^{2}}}{{{\mu }_{0}}}$

Answer 1

Hint: Energy stored in the inductor is due to current flowing through the inductor which generates the magnetic field. Energy stored in the inductor doesn’t get lost if the inductor is 100% efficient. When the current through the inductor is turned down then the energy returns to the rest of the circuit. You need to apply the formula of inductance and current in
$W=\dfrac{1}{2}L{{I}^{2}}$
To find magnetic energy stored per unit volume, you need to separate a volume quantity out of the formula.

Complete step by step answer:
Energy stored in an inductor = $\dfrac{1}{2}L{{I}^{2}}$
Inductance is defined as the ratio of the induced voltage to the rate of change of current in the conductor. The best example of an inductor is a coil of wire. Inductor in a circuit diagram is represented as a coil as well. There are two types of inductance ie., self-inductance and mutual inductance.
Self-inductance is defined as the voltage induced in a conductor due to the changing current in the conductor itself.
Mutual inductance is defined as the voltage induced in a coil due to the magnetic field interaction with another coil.
$W=\dfrac{1}{2}L{{I}^{2}}$
$W=\dfrac{1}{2}\times \dfrac{{{\mu }_{0}}{{N}^{2}}A}{l}\times {{(\dfrac{Bl}{{{\mu }_{0}}N})}^{2}}$
$=\dfrac{{{B}^{2}}}{2{{\mu }_{0}}}lA$ (since lA is equal to volume)
Therefore Magnetic energy stored per unit volume =$\dfrac{{{B}^{2}}}{2{{\mu }_{0}}}$.

Note:
In electromagnetism and electronics, inductance is the attribute of a conductor to oppose a change in the electric current flowing through it. A magnetic field is created around the conductor when electric current flows through it. The field strength depends on the magnitude of the current. Any changes in the current results in change of the field strength. From Faraday's law of induction, an electromotive force is generated in the conductor if there is any change in current, a process known as electromagnetic induction.