Spread the love

Gauss Law in Magnetism

Gauss Law in Magnetism :- Pay attention to the field lines of electric-dipole and magnetic-dipole in the picture given in the article Properties of Magnetic Field Lines :-

In the above figure (C), as many electric field lines enter the closed Gaussian surface L₂ as they emerge from it. This is because the magnitude of the total charge surrounded by this surface is zero. But in the same figure (c), for the closed Gaussian surface L₁ which confines the positive charge, the resultant output electric flux is non-zero. This is because electric field lines do not form a continuous loop.

Now if we observe the above figure (A) or (B) we will find that the situation is completely different for the magnetic field lines, which are continuous and form a closed loop. In figure (A) or (B), the number of magnetic field lines emanating from the closed surfaces L₁ and L₂ is equal to the number of field lines entering these surfaces. The total magnetic flux for both surfaces is zero and this is true for any closed surface along the magnetic field lines.

In the above figure the magnetic flux passing through the area ds is :-

$\displaystyle d{{\phi }_{B}}=\overrightarrow{B}.\overrightarrow{ds}=Bds\cos \theta$

If we divide the given surface into many similar small components ds and calculate the values of fluxes passing through each of them separately and integrate them, then we will get the total magnetic flux zero :-

$\displaystyle {{\phi }_{B}}=\oint{d{{\phi }_{B}}}=\oint{\overrightarrow{B}.\overrightarrow{ds}}=\oint{Bds\cos \theta =0}$

Therefore, according to Gauss’s law in magnetism, the value of total magnetic flux associated with a closed surface is always zero.

This is in contrast to Gauss’s law in electrostatics where the electric flux passing through a closed surface is given by the following formula :-

$\displaystyle {{\phi }_{E}}=\oint{d{{\phi }_{E}}}=\oint{\overrightarrow{E}.\overrightarrow{ds}}=\oint{Eds\cos \theta =\frac{q}{{{\varepsilon }_{0}}}}$

Where q is the charge enclosed by the closed surface.

The difference between Gauss’s laws of magnetism and electrostatics expresses the fact that single magnetic poles (monopoles) do not exist in magnetism.

Electric field lines have an origin and sinks, but magnetic field lines have no origin or sinks.

Gauss Law in Magnetism

Like this: