# Tangent Law of Magnetism

The early Aryan and Greek Philosophers were acquainted with the attractive property of natural magnets. As early as 120 A.D. it was found that an iron ore called magnetite attracted small pieces of iron, cobalt, nickel and the name 'magnets' was given to the pieces of this ore. The study of properties exhibited by these magnets was termed as 'magnetism'. A small magnet of an elongated shape, pivoted on a pin point, left to itself,automatically turns so that one of its ends points to the north and the other to the south. This is known as magnetic compass needle and is widely used as a navigational aid in ships and jet liners to know the direction of motion.

When a magnet is kept at a place, the space around it gets modified and it becomes a seat of energy. If another magnet is brought into this space it is acted upon by  a force due to this energy. Then the space around the magnet is said to be associated with a field known as magnetic field. Magnetic field can be defined as that which can exert a magnetic force and can produce magnetic induction in the matter placed in it. This magnetic induction is defined as a vector B.

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## Tangent Law

Superposition of two magnetic fields at right angles to each other gives rise to the tangent law. Let a magnetic needle of magnetic moment M be pivoted initially along the horizontal components of earth's magnetic field BH . Now let a uniform magnetic field B be applied on the needle in a direction perpendicular to BH simultaneously. The magnetic needle experiences a couple due to the magnetic field 'B' and gets deflected from the magnetic meridian. The horizontal component of earth's magnetic field BH produces a restoring couple on the needle and tries to bring it back into the magnetic meridian. The needle will come to equilibrium at an angle `theta`  with BH , where the deflecting couple balances the restoring couple.

Then, the deflecting couple   =  MB sin(900 - `theta` )  =  MB cos `theta`.

The restoring couple      =    MBH  sin `theta` .

For equilibrium of the needle,   MB cos `theta`    =      MBH  sin `theta` .

`:.`       B    =   BH `(sintheta)/(costheta)`

B  =  BH tan`theta` .

This equation is pronounced as Tangent Law.

## Tangent Law of Magnetism:

The law states that, if a magnetic field 'B' is applied at right angles to the horizontal component of the earth's field BH , the needle comes to equilibrium at an angle `theta`  to the magnetic meridian such that,

tan`theta`    =   `(B)/(Bh)` .

The tangent law is used for comparing the magnetic fields which are mutually perpendicular and hence to compare the magnetic moments of two bar magnets using Deflection Magnetometer.

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