Question

Gauss's Law for Magnetic Fields says that magnetic flux is always zero. Faraday's Law says that a changing magnetic flux through a closed surface is equal to the induced electric field around that surface. But if magnetic flux is always zero, how can it ever change? Explain in detail.

Answer 1

Gauss's Law for Magnetism states that the magnetic flux through any closed surface is always zero. However, the magnetic flux can change over time, resulting in the induction of an electric field.

Step-by-step explanation:

Gauss's Law for Magnetism states that the magnetic flux through any closed surface is always zero. This means that the total number of magnetic field lines entering a closed surface is equal to the total number of field lines leaving that surface. However, this does not mean that magnetic flux cannot change.

Faraday's Law of Induction states that a changing magnetic flux through a closed surface induces an electric field. The change in magnetic flux can be achieved by changing the strength or direction of the magnetic field, or by changing the area of the surface through which the magnetic field passes.

So, even though the magnetic flux is always zero, it can change over time, resulting in the induction of an electric field.

Answer 2

Step-by-step explanation:

Gauss's law of magnetism is given as

`int B. dA = 0`

here it is surface integral of magnetic field in a 3 Dimensional closed loop

So in this type of 3D closed loop number of linens of magnetic field is always zero because it always forms closed loops

Now as per Faraday's law

`\int E . dl = A(dB)/(dt)`

here we have to find the closed integral of 2 D planar loop of electric field which will be equal to potential difference

So this is non zero because total number of lines through a planar loop is not essentially zero.