Ampere's Law : The line integral magnetic induction (B) ar | Dr. Sajid Ali

Ampere's Law :

The line integral magnetic induction (B) around any closed path or circuit (imaginary or real like wire loop) is equal to µo (permeability of free space) times the total current (I) flowing through the are bounded by closed curve.

Mathematicaly,∫ B dl=µo I

The closed loop is called an Amperean loop Ampere's law is a scalar equation and is analogous to Gauss's theo rem in electrostatics.

Applications of Ampere's law:
1) Magnetic field (induction) due to straight conductor car rying current, at a point at distance r from it is,

B= µoI/ 2πr =µo/4π × 2I/r

2) The magnetic induction at a point well inside a solenoid along its axis is B=H, n I, where n is the number of turns per unit length of the solenoid. Instead of air if another medium permeability µ is kept then magnetic induction at the centre of solenoid is B = μnl.
for a point near the end of solenoid

B = µonl /2

3) The magnetic induction (B) inside the toroid is given

by B = μo nl

where n is the number of turns per unit length carrying current I.

By - @Dr. Sajid Ali