# Fun with Naughty Coil

The magnetic flux through a coil of cross-section area $$A$$ having $$N$$ turns and placed in a perpendicular magnetic field $$B$$ is given by $$\phi=NBA$$. According to Faraday's law of electromagnetic induction, the induced emf in a coil is proportional to the rate of change of magnetic flux through the coil.

## Procedure

One normal coil, one naughty coil, magnet, galvanometer, and connecting wires for this demonstration.

Connect the normal coil (say coil 1) and naughty coil (say coil 2) in series. Connect the galvanometer as shown in the figure. Take a magnet and make it pass through the coil 1. You will notice the deflection of the galvanometer. Now, make the magnet pass through the coil 2. You will not see deflection of the galvanometer this time. What could be the reason for it? Note that two coil are identical in shape and size, uses same wire, and have same number of turns.

## Discussion

The naughty coil is different from other coil in its construction. The net magnetic flux through the naughty coil is zero. It has half number of turns ($$N/2$$) in clockwise direction and another half ($$N/2$$) in anticlockwise direction. The magnetic flux is given by $$\phi=\vec{B}\cdot\vec{A}$$. The area vector $$\vec{A}$$ is in opposite directions in two halves of the naughty coil. Thus, magnetic flux through one half is $$BAN/2$$ and another half is $$-BAN/2$$ making net magnetic flux through the coil zero.

You can also think of naughty coil as made up of two similar coil connected in series. The induced emf in one half is $$e$$ and in another half is $$-e$$ making net induced emf zero.

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