Question

If magnetic monopoles existed, then which of the following Maxwell's equations would be modified?

• A. $\oint \vec{E} \cdot \overrightarrow{d s}=\frac{q}{\varepsilon_{0}}$
• B. $\oint \vec{B} \cdot \vec{d} s=0$
• C. $\oint \vec{E} \cdot \overrightarrow{d l}=\frac{d}{d t} \int \vec{B} \cdot \vec{d} s$
• D. $\oint \vec{B} \cdot \overrightarrow{d l}=\mu_{0} \epsilon_{0} \frac{d}{d t} \int \vec{E} \cdot \overrightarrow{d s}+\mu_{0} i$

Answer 1

Answer: (B)

If magnetic monopole existed, then the Guass' law for magnetism will get modified.
In that case, $\oint \vec{B} \cdot \vec{d} s=\frac{q_{m}}{\epsilon_{0}},$ where $q_{m}$ is the magnetic charge.