Question

On a clear day at a certain location, a 119-V/m vertical electric field exists near the Earth's surface. At the same place, the Earth's magnetic field has a magnitude of 5.050 10-5 T.

(a) Compute the energy density of the electric field. nJ/m3
(b) Compute the energy density of the magnetic field. µJ/m3

Answer 1

(a) 62.69 nJ/m^3

(b) 1015.22 μJ/m^3

Step-by-step explanation:

Electric field, E = 119 V/m

Magnetic field, B = 5.050 x 10^-5 T

(a) Energy density of electric field =
`(1)/(2)\varepsilon _(0)E^(2)`

`=(1)/(2)* 8.854* 10^(-12)* 119* 119`

= 6.269 x 10^-8 J/m^3 = 62.69 nJ/m^3

(b) energy density of magnetic field =
`(B^(2))/(2\mu _(0))`

`=(\left ( 5.05* 10^(-5) \right )^(2))/(2* 4* 3.14* 10^(-7))`

= 1.01522 x 10^-3 J/m^3 = 1015.22 μJ/m^3