Question

A coil of wire has been wrapped into a circle of 100 times with a diameter of 2.0 m. The coil is placed in a magnetic field of 5.0T perpendicular to the plane of the loop. The loop is suddenly flipped 180° in 2.0 seconds. What is the average emf induced in the loop?

Answer 1

Answer:

1570 V

Explanation:

N = 100

diameter = 2 m

radius = 1 m

B = 5 tesla

initailly the angle between the area vector of the coil and the magnetic field is zero and then the angle becomes 180 degree.

t = 2 s

Let Φ be the initial magnetic flux.

Φ = B A Cos 0 = 5 x 3.14 x 1 x 1 x 1 = 15.7 Wb

Let Φ' be the final magnetic flux

Φ' = B A Cos 180 = - 5 x 3,14 x 1 x 1 x 1 = - 15.7 Wb

According to the law of electromagnetic induction, the induced emf developed is equal to the rate of change of magnetic flux linked with the coil.

$e = -N\frac{d\phi }{dt}=\frac{\phi '-\phi }{t}$

$e =-100\frac{-15.7-15.7}{2}=1570 V$