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A solenoid is made out of a current-carrying wire which is coiled into a series of turns. In a solenoid, a large field is produced parallel to the axis of the solenoid. Components of the magnetic field in other directions are cancelled by opposing fields from neighboring coils. Outside the solenoid the field is also very weak due to this cancellation effect and for a solenoid which is long in comparison to its diameter; the field is very close to zero. Inside the solenoid the fields from individual coils add together to form a very strong field along the center of the solenoid.
The magnetic field due to a solenoid is given by,
Here, n = number of turns per unit length and I = amount of electric current passing through the solenoid.
This law implies that the magnetic field in space around an electric current is proportional to the electric current which serves as its source just as the electric field in space is proportional to the charge which serves as its source. This law states that for any closed loop path, the sum of the length elements times the magnetic field in the direction of length element is equal to the permeability times the electric current flowing in the loop.
In integral form it is written as follows:
This expression implies that the line integral of magnetic field around a closed loop is equal to the permeability times the electric current flowing through the loop.
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