Question

Which of the following field equations indicate that the free magnetic charge do not exist

• A. $\overrightarrow{H}=\frac{1}{\mu }▽\times \overrightarrow{A}$
• B. $\overrightarrow{H}=\oint \frac{I\overrightarrow{dl}\times \overrightarrow{R}}{4\pi R^2}$
• C. $▽.\overrightarrow{H}=0$
• D. $▽\times \overrightarrow{H}=\overrightarrow{J}$

Answer 1

The correct option is C

$▽.\overrightarrow{H}=0$

Ans : (c)

Magnitic field lines are closed around the current and have no sources or sink points.

$\nabla \cdot B=0$

$\underset{s}{\oint }\overrightarrow{B}\cdot \overrightarrow{dS}=0$

$\nabla \cdot \overrightarrow{B}=0$
In any closed surface,
Entering flux = Leaving flux
Dipole is the cause of magnetic fields.
Magnetic monopoles or free charges do not exist is justified by
$\nabla \cdot \overrightarrow{B}=0$ .
According to the Gauss's law for magneitc fields.
$\underset{s}{\oint }\overrightarrow{B}\cdot \overrightarrow{dS}=0$

$\nabla \cdot \overrightarrow{B}=0$

$\nabla \cdot \mu \overrightarrow{H}=0$

$\mu \nabla \cdot \overrightarrow{H}=0$

$\nabla \cdot \overrightarrow{H}=0$