In: Physics
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?
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.