A coil of wire with 50 turns lies in the plane of the page and has an initial area of 0.180 m2. The coil is now stretched to have no area in 0.100 s. What is the magnitude and direction of the average value of the induced emf if the uniform magnetic field points into the page and has a strength of 1.51 T

Explanation:

Given that,

Number of turns of coil

N = 50 turns

Initial area of plane

A1 = 0.18 m²

The coil it stretch to a no area in time t = 0.1s

No area implies that the final area is 0, A2 = 0 m²

Constant magnetic field strength

B = 1.51 T

EMF?

EMF is given as

Using far away Lenz law

ε = —N• dΦ/dt

Where Φ = BA

Then,

ε = —N• d(BA)/dt

Since B is constant,

ε = —N•B dA/dt

ε = —N•B (∆A/∆t)

ε = —N•B(A2—A1)/(t2-t1)

ε = —50 × 1.51 (0—0.18)/(0.1—0)

ε =—75.5 × —0.18 / 0.1

ε = 135.9 V

The induced EMF is 135.9V

Fleming’s left hand rule stated that if the index finger points toward magnetic flux, the thumb towards the motion of the conductor, then the middle finger points towards the induced emf.

Since the area lines in the plane, then the induced emf will be out of the page