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A four-turn circular wire coil of radius 0.550 m lies in a plane perpendicular to a...

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Physics

A four-turn circular wire coil of radius 0.550 m lies in a planeperpendicular to a uniform magnetic field of magnitude 0.355 T. Ifthe wire is reshaped from a four-turn circle to a two-turn circlein 0.128 s (while remaining in the same plane), what is the averageinduced emf in the wire during this time?

Answer & Explanation Solved by verified expert
4.0 Ratings (730 Votes)

According to the given problem,

We know that,

Induced EMF   E   =   -dφ/dt   =   - B *dA/dt   =   - B * (A2 -A1) / dt   =   B *(A1   -   A2) /dt

Given,

B   =   Magneticfield   =   0.355 T,   

   In reshaping of wire, circumference ( totallength) must remain the same.

   When wire is in four loops,   totallength   L   = 4 *(2 * π *r1 )  = 8 *π *0.55 = 13.823 m

   When wire is in two loop   L   = 2(2 *π *r2) =>   r2   = 13.823/4*π = 1.1 m

   Initialarea   A1   =   No.of loops * π *r12   = 4 *3.14 *0.552   = 3.80133 m2

   Finalarea   A2   = No.of loops* π*r22   = 2* 3.14*1.12   = 7.6027 m2

   Hence inducedEMF   E   =   0.355 *( 3.80133  -   7.6027) /0.128 =    - 10.543 V

   - ve sign idicates the direction of inducedEMF.
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