Q.What is tangent law? Discuss in detail.

Step 1. Tangent law: a magnetic needle freely suspended in two mutually perpendicular uniform fields settles along their resultant, at angle $\theta$ from one field such that $B=B_H\tan\theta$.

Step 2. Instrument: a tangent galvanometer places a pivoted compass needle exactly at the centre of a vertical current-carrying coil; with no current, the needle rests along $B_H$; with current, the coil's own field $B=\mu_0NI/2R$ acts perpendicular to $B_H$.

Step 3. The needle deflects to angle $\theta$ where $B=B_H\tan\theta$, i.e. $\dfrac{\mu_0NI}{2R}=B_H\tan\theta$. …

• Forgetting the tangent galvanometer's coil must lie in the magnetic meridian for the tw …