# CBSE Class 12-science Answered

State ampere’s circuital law and express it mathmatically.

Ampere’s law states that the path integral or line integral over a closed loop of the magnetic field produced by a current distribution is given by

_{} where I refers to the current enclosed by the loop.

Ampere’s law is a useful relation that is analogous to Gauss’s law of electrostatics. It is a relation between the tangential component of magnetic field at points on a closed curve and the net current through the area bounded by the curve.

To evaluate the expression for _{}, let us consider a long, straight conductor carrying a current I, passing through the centre of a circle of radius r in a plane perpendicular to the conductor.

According to Biot-Savart law of magnetism, the field has a magnitude _{} at every point on the circle, and it is tangent to the circle at each point.

The line integral of _{} around the circle is

_{}

Since _{ }is the circumference of the circle,

Therefore, _{}