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# A circular coil (670 turns, radius = 0.079 m) is rotating in a uniform magnetic field. At t = 0 s, the normal to the coi...

A circular coil (670 turns, radius = 0.079 m) is rotating in a uniform magnetic field. At t = 0 s, the normal to the coil is perpendicular to the magnetic field. At t = 0.020 s, the normal makes an angle of 45 degrees with the field because the coil has made one-eighth of a revolution. An average emf of magnitude 0.052 V is induced in the coil. Find the magnitude of the magnetic field at the location of the coil.

Given data:

• Number of turns is N=670.
• Radius of coil is r=0.079 m.
• Angle made at $∆$t=0.020 s is $\theta =45°$.
• Emf induced is .

The magnetic flux is given by,

The induced emf in the coil is,

$\epsilon =\left|-N\frac{∆\varphi }{∆t}\right|\phantom{\rule{0ex}{0ex}}\epsilon =N\frac{∆\varphi }{∆t}$

Substitute all value in above expression,

Thus, the magnitude of magnetic field is $\begin{array}{rcl}& & 1\end{array}\begin{array}{rcl}& & .\end{array}\begin{array}{rcl}& & 12\end{array}\begin{array}{rcl}& & ×\end{array}\begin{array}{rcl}& & 10\end{array}\begin{array}{rcl}& & \end{array}$-4 T.

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