Question

A coil of wire is placed in a changing magnetic field. If the number of turns in the coil is decreased, what happens to the voltage induced across the coil ?
A. increases
B. decreases
C. remain constant
D. be excessive

Answer 1

Hint- Faraday's law states that induced EMF in a coil is equal to the negative of the rate of change of magnetic flux linked with the coil multiplied by the number of turns in the coil. It is given by the equation
$\varepsilon = - N\dfrac{{d\phi }}{{dt}}$
where $N$ is the number of turns of the coil and $\dfrac{{d\phi }}{{dt}}$is the rate of change of magnetic flux

Step by step solution:
EMF induced in a coil is given by Faraday's law.
Faraday's law states that induced EMF in a coil is equal to the negative of the rate of change of magnetic flux linked with the coil multiplied by the number of turns in the coil. It is given by the equation
$\varepsilon = - N\dfrac{{d\phi }}{{dt}}$
Take the magnitude,
$\left| \varepsilon \right| = N\dfrac{{d\phi }}{{dt}}$
where $N$ is the number of turns of the coil and $\dfrac{{d\phi }}{{dt}}$is the rate of change of magnetic flux
Therefore, if the number of turns of the coil is decreased then the value of voltage induced in the coil will also decrease.

So the answer is option B.

Note: The minus sign in the faraday's law is accounted for by Lenz's law. According to Lenz’s law the polarity of induced EMF is such that it opposes the change in magnetic field which produces it. When we want to know the magnitude of induced EMF we can ignore the minus sign since it only denotes the direction of induced EMF. That is why in this question we took the magnitude only to find whether the induced voltage decreases or increases when number of turns of the coil is decreased