Question

$\frac{B^2}{{\mu }_0}$ has the unit of :

• A. energy
• B. energy density
• C. potential
• D. capacity

Answer 1

The correct option is B energy density

Energy stored $=$ $\frac{1}{2}L{I}^2$ $L=$inductance of solenoid
$\frac{{\mu }_0{N}^{2}A}{l}$
Energy Density $=$ $\frac{\frac{1}{2}L{I}^2}{AL}$ $l=$$lengthofthesolenoidA$=$crossectionareaN$=$noofturnsB$=$Magneticfield$=\dfrac{\dfrac{1}{2}\dfrac{\mu _{0}N^{2}A}{l}\times \dfrac{B^{2}l^{2}}{\mu {_{0}}^{2}N^{2}}}{Al}=\dfrac{1}{2}\dfrac{B^{2}}{\mu _{0}}$