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CBSE Class 12-science Answered

In this question I am not able to understand that why the area of circle is not constant whereas the area of rectangle is constant.
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Asked by Balbir | 02 Mar, 2018, 11:02: PM
answered-by-expert Expert Answer
This question does not say that area of rectangle is constant and area of circle is not constant. What it says is rate of change of area of rectangle is constant. Similarly it says that rate of change of area of circle is not constant
To understand these statements, I have given the figure above for rectangular loop and circular loop. Let us assume the magnetic field is represented by shaded area. It can be seen from the figure, for rectangular loop, there is a steady rate of decrease of shaded area at each time interval dt.
In the case of circular loop, due to its shape, the rate of decrease of shaded area is not constant at different time interval dt.
 
induced emf begin mathsize 12px style equals negative fraction numerator d ϕ over denominator d t end fraction space equals space minus fraction numerator d left parenthesis B cross times A right parenthesis over denominator d t end fraction space equals space minus B fraction numerator d A over denominator d t end fraction end style
hence in rectangular loop, when the loop is exiting the magnetic field region, induced emf is constant because dA/dt is constant
but in circular loop, when the loop is exiting the magnetic field region, induced emf is varying because dA/dt is not constant
Answered by Thiyagarajan K | 03 Mar, 2018, 11:21: AM

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