# Ampere Circuital Law | Define | Formula

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# Ampere’s Circuital Law-

Ampere’s Circuital law provides us a shortcut method for finding the magnetic field due to infinitely long symmetrical bodies like infinitely long straight wire, infinitely long solenoid, infinite sheet etc.

 Ampere’s Circuital law states that- The line integral of the magnetic field over any closed loop is equal to μ0 times the net current passing through the area enclosed by this closed loop.

#### Mathematically,

The integral on the left hand side is called the magnetic induction.

 Ampere’s Circuital law can also be stated as- The magnetic circulation around a closed loop is μ0 times the net current enclosed by the loop.

The closed loop on which the law is applied is called as amperian loop.

## Selection of Amperian Loop-

The selection of the amperian loop is critical for easy application of the law. The general rules for selecting the amperian loop are-

### Rule-01:

The loop should include the current carrying element whose magnetic field is to be calculated.

### Rule-02:

The point or points at which the magnetic field is to be calculated must lie on the loop.

### Rule-03:

The loop should have enough symmetry so that the integral on LHS of the law can be easily calculated.

### Rule-04:

The magnetic field should be constant over the whole loop or should be easy to calculate on different portions of the loop.

### Rule-05:

Estimate the direction of magnetic field around the current carrying conductor before applying the law.

## Sign Convention-

While applying the ampere’s circuital law, the following right hand convention is to be used-

• current into the plane of paper is taken negative
• current out of the plane of paper is taken positive
• circulation in anticlockwise direction is taken positive
• circulation in clockwise direction is taken negative.

## Important Notes-

### Note-01:

If B is everywhere tangent to the integration path and has the same magnitude B at every point on the path, then its line integral is equal to B multiplied by the circumference of the path.

### Note-02:

• In the line integral ∮B.dℓ, B is always the total magnetic field at each point on the path.
• In general, this magnetic field is caused partly by currents enclosed by the path and partly by currents outside.
• Even when no current is enclosed by the loop, the magnetic field at points on the loop need not be zero. In that case, however ∮B.dℓ is always zero.

#### MCQs Quiz-

MCQs Quiz on Ampere’s Circuital Law

#### Worksheet-

Worksheet on Ampere’s Circuital Law

#### Next Article-

Magnetic Field Due To Long Thin Straight Wire

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