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What must be the magnitude of a uniform electric field if it is to have the same energy density as that possessed by a 0.50 T magnetic field?

Short Answer

Expert verified

1.5×108V/m

Step by step solution

01

Given

Magnetic fieldb=0.50T

02

Understanding the concept

We use the formula of energy density in the magnetic field and energy density in an electric field to find the magnitude of a uniform electric field if it is to have the same energy density as that possessed by amagnetic field.

Formula:

uE=12ε0E2uB=12B2u0

03

Calculate the magnitude of a uniform electric field required

The electric field density is given by

uE=12ε0E2

The magnetic field density is given by

uB=12B2u0

According to the given condition,

uE=uB12ε0E2=12B2u0E2=B2μ0ε0E=Bμ0ε0E=0.50T8.85×10-12F/m4π×10-7H/mE=1.5×108V/m

Therefore, the magnitude of a uniform electric field is 1.5×108V/m.

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