Question

A 41-turn square coil of area 0.074 m2 and a 123-turn circular coil are both placed perpendicular to the same changing magnetic field. The voltage induced in each of the coils is the same. What is the area of the circular coil?

Answer 1

Answer:

The area of second coil is ≅ 0.025 $m^{2}$

Explanation:

Given :

No. of turns in the first coil $N_{1} = 41$

No. of turns in the second coil $N_{2} = 123$

Area of first coil $A_{1} = 0.074 m^{2}$

According to the law of electromagnetic induction,

Induced emf = $-N \frac{d \phi}{dt}$

Where $\phi =$ magnetic flux.

Since given in question emf of both coil is same so we compare above equation.

    $-\frac{N_{1} d\phi _{1} }{dt_{1} } = -\frac{N_{2} d\phi _{2} }{dt_{2} }$

   $\frac{N_{1} A_{1} dB_{1} }{dt_{1} } = \frac{N_{2} A_{2} dB_{2} }{dt_{2} }$

        $A_{2} = \frac{N_{1} A_{1} }{N _{2} }$

        $A_{2} = \frac{41 \times 0.074 }{123 }$

        $A_{2} = 0.0246 = 0.025 m^{2}$

Therefore, the area of second coil is ≅ 0.025 $m^{2}$