Magnetic field energy

Electricity and Magnetism Level 3

An electromagnetic wave has a magnetic field component with an amplitude of B = 2 2 mT . B=2\sqrt{2} \text{ mT}. How much magnetic energy exists in π m 3 \pi \text{ m}^3 of space?


The answer is 10.

July Thomas by July Thomas , 30, USA

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2 solutions

July Thomas
Jun 26, 2016

Magnetic energy density is u B = B 2 2 μ 0 . u_B = \frac{B^2}{2\mu_0}.

Since magnetic energy density is the energy per unit volume, the total energy is

U = u B V = ( B 2 2 μ 0 ) ( V ) = ( ( 2 2 ) 2 2 μ 0 ) ( π ) = 10 J \begin{aligned} U &= u_B V \\ &= \big( \frac{B^2}{2\mu_0} \big) (V) \\ &= \big( \frac{(2\sqrt{2})^2}{2\mu_0} \big) (\pi) \\ &= 10 \text{ J} \end{aligned}

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(pi m^3) B^2 / (2 mu0) = 10 J. ez

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