A coil formed by wrapping 65 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 µT to 600 µT in 0.400 s, an emf of magnitude 80.0 mV is induced in the coil. What is the total length of the wire?

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cjmejiab cjmejiab · Answer 1 · 2020-04-23T06:13:44+02:00

To solve the problem, it is necessary to apply the concepts related to Faraday's law, for which the voltage induced on a body is defined as follows,

[tex]\epsilon = NA(cos\theta) (\frac{\Delta B}{\Delta t})[/tex]

Here,

N = Number of loops

A = Area

[tex]\Delta B[/tex] = Magnetic Field

[tex]\Delta t[/tex] = Time

[tex]\theta[/tex] = Angle between the magnetic field and the surface

Replacing,

[tex]A = \dfrac{\epsilon}{Ncos\theta (\frac{\Delta B}{\Delta t})}[/tex]

[tex]A = \dfrac{80.0mV}{(65)cos(30) (\frac{600\mu T-200\mu T}{0.4})}[/tex]

[tex]A = 1.42m^2[/tex]

Each side of the coil has a length of

[tex]d = \sqrt{A}[/tex]

Then the total length of the wire,

[tex]L = N(4d)[/tex]

[tex]L = 4N\sqrt{A}[/tex]

[tex]L = (4)(65)\sqrt{1.42}[/tex]

[tex]L = 308.95m[/tex]

Therefore the total length of the wire is 308.95m