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  4. A toroid has 500 turns per metre length. If it carries a current of 2A, the magnetic energy density inside the toroid is

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Q. A toroid has 500 turns per metre length. If it carries a current of 2A, the magnetic energy density inside the toroid is

KCETKCET 2019Moving Charges and Magnetism

Solution:

Magnetic field inside a toroid
$B=\mu_{0} nl$
Magnetic energy density inside the toroid is
$u_{0}=\frac{B^{2}}{2 \mu_{0}}=\frac{\mu _{0} ^{2}n^{2} I^{2}}{2 \mu_{0}}=\frac{\mu_{0}n^{2}I^{2}}{2}$
$=\frac{4\pi\times10^{-7}\times\left(500\right)^{2}\times2^{2}}{2}=0.628 \, J m^{-3}$