Question

It is proposed to store 1.00kW⋅h=3.60×106J of electrical energy in a uniform magnetic field with magnitude 0.550 T . What volume (in vacuum) must the magnetic field occupy to store this amount of energy?

Answer 1

Answer:

$V=29.9\ m^3$

Explanation:

Given that,

Magnetic field strength, B = 0.55 T

Energy stored, $E=3.6\times 10^6\ J$

To find,

The magnetic field occupy to store this amount of energy.

Solution,

We know that the magnetic energy per unit volume in the magnetic field is given by :

$\dfrac{E}{V}=\dfrac{B^2}{2\mu_o}$

$\dfrac{3.6\times 10^6}{V}=\dfrac{(0.55)^2}{2\times 4\pi \times 10^{-7}}$

$V=29.9\ m^3$

So, the volume in the vacuum is $29.9\ m^3$. Hence, this is the required solution.