At a particular point and instant, the magnetic field component of an electromagnetic wave is $15.0$ $\mu \mathrm { T }$. What is the magnetic energy density of this wave at that point and instant? $\left( c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } \right.$, $\mu _ { 0 } = 4 \pi \times 10 ^ { - 7 } \mathrm {~T} \cdot \mathrm { m } / \mathrm { A } , \varepsilon _ { 0 } = 8.85 \times 10 ^ { - 12 } \mathrm { C } ^ { 2 } / \mathrm { N } \cdot \mathrm { m } ^ { 2 }$ )
A) $2.26 \times 10 ^ { - 4 } \mathrm {~J} / \mathrm { m } ^ { 3 }$
B) $4.47 \times 10 ^ { - 4 } \mathrm {~J} / \mathrm { m } ^ { 3 }$
C) $1.79 \times 10 ^ { - 4 } \mathrm {~J} / \mathrm { m } ^ { 3 }$
D) $8.95 \times 10 ^ { - 5 } \mathrm {~J} / \mathrm { m } ^ { 3 }$
E) $9.72 \times 10 ^ { - 5 } \mathrm {~J} / \mathrm { m } ^ { 3 }$

Question

Quizplus · Accepted Answer

The magnetic energy density $ u_B $ is given by $ u_B = \frac{B^2}{2\mu_0} $. Substituting $ B = 15.0 \times 10^{-6} \, \mathrm{T} $ and $ \mu_0 = 4\pi \times 10^{-7} \, \mathrm{T \cdot m/A} $, we get $ u_B = \frac{(15.0 \times 10^{-6})^2}{2 \times 4\pi \times 10^{-7}} \approx 8.95 \times 10^{-5} \, \mathrm{J/m^3} $.

At a Particular Point and Instant, the Magnetic Field Component 15.015.015.0

At a Particular Point and Instant, the Magnetic Field Component $15.0$