Question

The earth's magnetic field, like any magnetic field, stores energy. The maximum strength of the earth's field is about 7.0 x 10-5 T. Find the maximum magnetic energy stored in the space above a city if the space occupies an area of 4.8 x 108 m2 and has a height of 1500 m.

Answer 1

1.4 x 10^9 J

Step-by-step explanation:

magnetic field, B = 7 x 10^-5 T

Area, A = 4.8 x 10^8 m^2

height, H = 1500 m

the formula for the energy density is given by

`u=(B^(2))/(2\mu _(0))`

Total energy = Energy density x Volume

`U=(B^(2))/(2\mu _(0))* A* H`

`U=(\left (7* 10^(-5)  \right )^(2))/(2* 4* 3.14* 10^(-7))* 4.8* 10^(8)* 1500`

U = 1.4 x 10^9 J

Thus, the maximum magnetic energy stored is 1.4 x 10^9 J