A magnetic needle suspended, at a point where there are two crossed magnetic fields acting at right angles to each other, will come to rest in the direction of the resultant of the two fields.

B_{1} and B_{2} are two uniform magnetic fields acting at right angles to each other. A magnetic needle placed in these two fields will be subjected to two torques tending to rotate the magnet in opposite directions. The torque τ_{1} due to the two equal and opposite parallel forces mB_{1} and mB_{1} tend to set the magnet parallel to B_{1}.

Similarly the torque τ_{2} due to the two equal and opposite parallel forces mB_{2} and mB_{2 }tends to set the magnet parallel to B_{2}. In a position where the torques balance each other, the magnet comes to rest. Now the magnet makes an angle θ with B_{2} as shown in the Figure.

The deflecting torque due to the forces mB_{1} and mB_{1}

**τ _{1} = mB_{1} x NA**

= mB_{1} x NS cos θ

= mB_{1} x 2Ɩ cos θ

= 2Ɩ mB_{1} cos θ

**So, τ _{1} = MB_{1} cos θ**

Similarly the restoring torque due to the forces mB_{2} and mB_{2}

**τ _{2} = mB_{2} x SA**

= mB_{2} x 2Ɩ sin θ

= 2Ɩ m x B_{2} sin θ

**so, τ _{2} = MB_{2} sin θ**

At equillibrium, τ_{1} = τ_{2}

**MB _{1} cos θ = MB_{2} sin θ**

so, **B _{1} = B_{2} tan θ**

**This is called Tangent law**

Invariably, in the applications of tangent law, the restoring magnetic field B_{2} is the horizontal component of Earth’s magnetic field B_{h}.