## Ampere’s Circuital Law

Ampere’s circuital law is one of the general laws of magnetism. This law used to find the magnetic field due to current distribution. Current distribution should have a high degree of symmetry.

Somehow Ampere’s law has similarity with the Gauss law of electricity but also quite simple.

Ampere’s circuital law establishes the relation between current and magnetic field. Electric current acts as a source for magnetic fields in a similar way as a charge acts as a source for electric fields. The value of the field is directly proportional to the strength of current.

**Statement**

Ampere’s Law states that

*The integral around a closed path of the component of the magnetic field tangent to the direction of the path equals μ _{0} times the current intercepted by the area within the path.*

………..(1)

Thus according to Ampere’s Law, the summation of the length elements times the magnetic field in the direction of the length element for any closed loop is equal to the permeability times the electric current flowing in the loop.

The equation (1) can take the form

** **** **** **** **………..(2)

Thus the line integral of the magnetic field around some arbitrary closed curve is equal to the total current enclosing that curve.

**In order to apply Ampere’s Law**

- All currents do not change with time i.e. it needs to be steady.
- Only those currents are taken into account which cross the area inside the path and have some contribution to the magnetic field.
- Current direction should be taken into account. Currents flowing outward of the surface are positive, those flowing inward to the surface are negative. Right hand’s rule is useful to determine directions and signs.

**In the following cases total magnetic circulation is zero**

- Net enclosed current is zero.
- If the magnetic field is normal to the path at any point.
- When magnetic field is zero.

Finally, it is important to note that Ampere’s Law can apply to magnetostatics only. Because If a time-varying electric field is present, there is an additional term known as the displacement current on the right side of the ACL.

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