A coil formed by wrapping 50 turns of wire in the shape of a square is positioned in a magnetic field so that the normal to the plane of the coil makes an angle of 30.0° with the direction of the field. When the magnetic field is increased uniformly from 200 μ T to 600 μ T in 0.400 s, an emf of magnitude 80.0 mV is induced in the coil. What is the total length of the wire in the coil?

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Physics for Scientists and Enginee...

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Raymond A. Serway + 1 other

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Physics for Scientists and Enginee...

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Raymond A. Serway + 1 other

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To determine

The total length of wire in the coil.

Explanation of Solution

Given info: Number of turns of wire is 50 , angle of the normal to the direction of field is 30 ° , Magnetic field is increasing from 200 μT to 600 μT in 0.400 s and emf induced in the coil is 80.0 mV .

The rate of increase in magnetic field with respect to time can be given as,

ΔBΔt=B2−B1t

Here,

B1 is the initial magnetic field.

B2 is the final magnetic field.

t is the time.

Substitute 200 μT for B1 , 600 μT for B2 and 0.400 s for t in the above equation,

ΔBΔt=(600 μT−200μT)(1 T106 μT)0.400 s=10−3 T/s

According to Faraday’s law of induction, the emf induced in a coil can be given as,

ε=NΔBΔtAcosθ=NΔBΔta2cosθ

Here,

N is the number of turns in coil

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