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

 

Get more notes & other study material of the Chapter Moving Charges & Magnetism.