# Effect of greater coils on induced current in a solenoid

Simple case:-

A bar magnet is inserted into a solenoid with 'n' turns at velocity 'v'. The current is measured using an ammeter that is part of the complete circuit of the solenoid.

My question is that if I increase the number of turns 'n' then will this lead to a greater induced pd and in turn, induced current detected by the ammeter.

Please could you provide a brief explanation as well because its not intuitive whether it will increase or decrease

• Increasing the number of turns also increases the resistance in the circuit. – Farcher May 28 '18 at 17:53

According to Faraday's law of electromagnetism, emf induced is given by

$\epsilon=\frac{d\phi}{dt}$

But $\phi=B.A$

Here B is the electric field and A is the effective area though which the electric flux changes.

$\therefore$effective area =$n.a$

Here a is the area of each turn and n is the number of turns of the coil.

$\therefore \epsilon = \frac{d(B.n.a)}{dt}$

$\implies \epsilon =n.a.\frac{dB}{dt}$

Therefore emf induced is directly proportional to the number of turns in the coil.

By ohm's law, the current in the circuit is proportional to emf across the conductor. Therefore the current, emf both increases with increase in number of turns.