Question

In: Physics

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

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

Solutions

Expert Solution

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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