Question

An emf is induced in a conducting loop of wire 1.12m long as its shape is changed from square to circular. Find the average magnitude of the induced emf if the change in shape occurs in 4.25 seconds and the local 0.105 T magnetic field is perpendicular to the plane of the loop.

Answer 1

Length of the wire L = 1.12 m

Let the side of the square be a thencircumference 4a = L

From this side a = 0.28 m

Area of the square A = a ^ 2= 0.0784 m ^ 2

Circumference of the loop 2(pi) r = L

From this radius of the loop r = L / 2 ( pi )

                                                = 0.17825 m ^ 2
Area of the loop A ' = πr ^ 2= 0.09982 m ^ 2

  Time interval dt = 4.25 s

Magnetic field B = 0.105 T

Average induced emf E = B dA / dt

                                    = B ( A ' - A ) / dt

                                    = 5.292 * 10^ -4 Volt