Question

how ampere's circuital law in magnetics is eequivalent to guass law in electrostatics​

Answer 1

Answer:

The answer is as follows:-

Explanation:

Ampere's Circuital Law: This law states that the line integral of magnetic field B around a closed path in vacuum is equal to

μo

times the the total current I threading the closed path.

1. B is to be written as B⃗ .

2. μo is to be written in the symbol form.

There is an alternative way to evaluate the magnetic field of a current carrying coil by applying Ampere's circuital law. This law is equivalent to Gauss Law in Electrostatics. By applying this law to current carrying straight solenoid and toroid one, can calculate the magnetic fields.

A solenoid is made up of a long insulating wire closely wound in the form of a helix. The length:width ratio of the solenoid is very large.

The toroid: Also known as an endless solenoid, is a hollow circular ring on which a large number of insulated turns of metallic wire are closely wound.

Answer 2

Answer:

Ampere's circuital law in magnetostatics is analogous to the Gauss's law in electrostatics.​    

Explanation:

Ampere's law in magnetostatics defines the magnetic field produced around a loop of current carrying conductor.

• The Ampere's circuital law states that the magnetic field along an imaginary closed path is equal to  $\mu_0$ times the current enclosed inside the closed path.

       $\oint \vec B.d\vec l =\mu_0I$

• where $\vec B$ is the magnetic field, $I$ is the electric current, $\mu_0$ is the magnetic permeability, and $d\vec l$ is the length of the conductor.
• It is used to measure the magnetic field.

Gauss's law in electrostatics​ defines the electric field generated by a distribution of electric charges.

• The Gauss's law states that the electric flux through a closed surface enclosing a volume is equal to the net electric charge enclosed by it.

        $\oint_s \vec E.d\vec s =\dfrac{Q}{\varepsilon_0}$

• where $\vec E$ is the electric field, $Q$ is the net charge, $\varepsilon _0$ is the electric permittivity, and $d\vec s$ is the elemental closed surface.
• It is used to measure the electric field.

Thus, Ampere's circuital law in magnetostatics is analogous to the Gauss's law in electrostatics.​    

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