The south pole of a bar magnet is moved toward a short helical coil of wire (solenoid) along the...

Question:

The south pole of a bar magnet is moved toward a short helical coil of wire (solenoid) along the axis of the coil. The coil has 100 turns and the ends of the coil are connected to form a closed circuit. If the coil is replaced with a single loop of the same type of wire, and the magnet is moved exactly as before, the current induced in the loop is how many times less?

Electromotive force:

Electromotive force is equivalent to the voltage created by non-electrical objects. The generation of electromotive force occurs due to changing magnetic field. EMF generates by the conversion of energy.

Given data

• Number of turns in coils is {eq}N = 100.{/eq}
• Electromotive force is {eq}\varepsilon .{/eq}

The expression for the Faraday's law of electromagnetic induction is,

{eq}\varepsilon = - N\dfrac{{d{\phi _B}}}{{dt}} {/eq}

The expression for the ohm's law is,

{eq}V = IR {/eq}

Substituting the given values,

{eq}\varepsilon = - 100\dfrac{{d{\phi _B}}}{{dt}}......\left( 1 \right) {/eq}

When the number of turns becomes one,

{eq}\varepsilon = - 1\dfrac{{d{\phi _B}}}{{dt}}......\left( 2 \right) {/eq}

Since, the values of electromotive force linearly varies with the number of turns and the electromotive force is equal to the applied voltage. Therefore if the number of turns is reduced to 100 times, the value of electromotive force becomes 100 times less. As voltage and current are directly related, so the value of current becomes 100 times less than the original.