Question

The net magnetic flux through any closed surface, kept in a magnetic field is
A. zero
B. \[\dfrac{{{\mu _0}}}{{4\pi }}\]
C. \[4\pi {\mu _0}\]
D. \[\dfrac{{4{\mu _0}}}{\pi }\]

Answer 1

Hint:In a closed surface, magnetic field lines enter into it, also at some point it also comes out to form a closed loop. That means every magnetic field line that enters the closed surface has the same field line that exits the closed surface. Therefore the magnetic flux through the closed surface is zero. In another words if we compute the magnetic flux through a closed surface as:\[\oint {\overrightarrow B \bullet dA = 0} \]

Formula used Magnetic flux is given as:
\[\varphi = B \bullet A\]
Where B is the magnetic field and A is the area.
In a closed surface magnetic field is:
\[\oint {\overrightarrow B \bullet dA = 0} \]

Complete step by step solution:
As the net magnetic flux through any closed surface is
\[\varphi = B \bullet A\]
In any closed surface kept in a uniform magnetic field, the magnetic field lines entering through it will equal the magnetic field leaving it. Hence we say that the number of magnetic field lines entering is equal to the magnetic field lines leaving through any closed surface. Therefore the net magnetic flux in a closed surface will be zero.

Hence option A is the correct answer.

Note: Gauss law explains the electric flux through a closed surface is equal to the enclosed charge divided by \[{\varepsilon _0}\]. The magnetic field lines don’t behave in the same manure as the electric field lines do. As magnetic field lines are in closed loops. It doesn’t mean every magnetic flux is zero. Due to the closed surface magnetic field is zero.