So the solution to this question has already been answered, I just dont understa

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So the solution to this question has already been answered, I just dont understand why they are using Area of a rectangle can someon explain this to me please

Chapter 22, Problem 14 Go. Solution Google Chrome Secure https:// wiley plus.com/edugen/shared/assignment/test/qsolution.un emid ares C22go-tutorial 1-2 edugen REASONING At any given moment, the flux D that passes through the loop is given by BAcoso (Equation 22,2), where B is the magnitude of the magnetic field, A is the area of the oop, and he angle between the normal to the loop and he direct on of the magnetic d (both directed nto the page As the handle turns, the area A of th oop changes causing a change A in the flux passing through the loop. We can think of the loop as being divided into a rectangular portion and a semicircular portion. Initially, the area Ao of the loop is equal to the Tr of the semicircle, where r is the radius of the semicircle Ao ec Tr After half a revolution, the semicircle is once again rectangular area rec plus the area Asemi A within the plane of the loop, but now as a reduction of the area of the rectangular portion. Therefore, the final area A of the loop is equal to the area of the rectangular portion minus the area of the semicircle BAcos$ uation 22.2) and the initial flux BAocos SOLUTION The change Ad in the flux that passes through the loop is the difference between the final flux Substituting A0 Arec lmr2 and A Inr m2) Area 2 Therefore the change in the flux passing through the loop during half a revolution of the semicircle is (0.30 m 0.90T) cos0 0.25 Wb Copyright C 2000-2017 by John Wiley & Sons, Inc. or related companies. All rights reserved 10 PM Ask me anything 2/28/2017

Explanation / Answer

Here the wire is in the form of rectangle and one side of rectangle has also a semi circle.

Now if semicircle is upwards then the total area is

Area = Area of rectangle + area of semi circle

When the semi circle is made downwards then we need to subtract its area from rectangle area in order to get the total area.

Reason being the consideration area of rectangle is simple as it is a part of the loop.

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