Question

Using \[B=\mu_0nI\], what is the magnetic energy density inside the air-core solenoid?

Options

• \[u_B=\frac{B}{2\mu_0}\]

• \[u_B=\frac{B^2}{2\mu_0}\]

• \[u_B=\frac{\mu_0B^2}{2}\]

• \[u_B=\frac{B^2}{\mu_0}\]

Answer 1

Squaring \[B=\mu_0nI\] gives \[B^2=\mu_0^2n^2I^2\]. Substitution into \[u_B=\frac{1}{2}\mu_0n^2I^2\] yields \[u_B=\frac{B^2}{2\mu_0}\].