What electric field has the same energy density as a $1.0 \mathrm{~T}$ magnetic field?
A) $1.1 \times 10-17 \mathrm{~V} / \mathrm{m}$
B) $9.0 \times 1016 \mathrm{~V} / \mathrm{m}$
C) $1.0 \mathrm{~V} / \mathrm{m}$
D) $3.0 \times 10^{8} \mathrm{~V} / \mathrm{m}$
E) $3.3 \times 10-9 \mathrm{~V} / \mathrm{m}$

Question

Quizplus · Accepted Answer

The energy density of a magnetic field ($u_B$) is given by $u_B = \frac{B^2}{2\mu_0}$, where $B$ is the magnetic field strength and $\mu_0$ is the permeability of free space ($4\pi \times 10^{-7} \, \text{N/A}^2$). For a $1.0 \, \text{T}$ magnetic field, $u_B = \frac{(1.0)^2}{2 \times 4\pi \times 10^{-7}} \, \text{J/m}^3$.The energy density of an electric field ($u_E$) is given by $u_E = \frac{\epsilon_0 E^2}{2}$, where $E$ is the electric field strength and $\epsilon_0$ is the permittivity of free space ($8.85 \times 10^{-12} \, \text{F/m}$).Setting $u_B = u_E$ and solving for $E$ gives an electric field strength that matches the energy density of a $1.0 \, \text{T}$ magnetic field. The correct magnitude for $E$ that matches the energy density of a $1.0 \, \text{T}$ magnetic field is $3.0 \times 10^{8} \, \text{V/m}$, which corresponds to choice D.

What Electric Field Has the Same Energy Density as A 1.0