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A rectangular loop of wire with sides 0.262 and 0.401 m lies in a plane perpendicular to a constant magnetic field (see part a of the drawing). The magnetic field has a magnitude of 0.764 T and is directed parallel to the normal of the loop's surface. In a time of 0.153 s, one-half of the loop is then folded back onto the other half, as indicated in part b of the drawing. Determine the magnitude of the average emf induced in the loop.

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akande212

Answer:

E = 0.262V

Explanation:

Given Area = 0.262m×0.401 m =0.105m², B = 0.764T, Δt = 0.153s

In this time interval the area is halved. This causes the flux to change with time and as a result induce an emf in the loop.

So

ΔФ = BΔA

ΔA = 1/2×0.105m² = –0.0525m²

ΔФ = –0.764×0.0525 = –0.04011Wb

ΔФ/Δt = –0.04011/ 0.153 = –0.262Wb/s

E = –(ΔФ/Δt) = –(–0.262) = 0.262V

E = 0.262V

The magnitude of the average emf induced in the rectangular loop is 0.262Wb/s which is explained below.

Induced EMF:

Given information:

length of the rectangle, L = 0.401 m

breadth of the rectangle, B = 0.262m

So Area:

A = 0.262m × 0.401 m

A = 0.105m²

magnetic field B = 0.764T,

time Δt = 0.153s

The area of the loop is halved after the given time, so now there is a change in the magnetic flux passing through the rectangle.

Change in flux:

dФ = BdA

or

ΔФ = BΔA

Now,

ΔA = 0.105m² - 1/2×0.105m² = 0.0525m²

So,

ΔФ = 0.764×0.0525

ΔФ = 0.04011Wb

The induced EMF is given by:

E = –(ΔФ/Δt)

E = –0.04011/ 0.153

E = –0.262Wb/s

The magnitude of EMF produced in the loop is 0.262Wb/s

Learn more about induced emf :

https://brainly.com/question/4721624?referrer=searchResults

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