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  4. A conducting circular loop is placed in a uniform magnetic field, B = 0.025 T with its plane perpendicular to the loop. The radius of the loop is made to shrink at a constant rate of text1 textmm texts-1. The induced emfwhen the radius is 2 cm, is

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Q. A conducting circular loop is placed in a uniform magnetic field, B = 0.025 T with its plane perpendicular to the loop. The radius of the loop is made to shrink at a constant rate of $ \text{1}\,\text{mm}{{\text{s}}^{-1}}. $ The induced emfwhen the radius is 2 cm, is

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Solution:

Magnetic flux $ \text{o}|=\,B.A $ $ =B.\pi {{r}^{2}} $ Induced emf, $ |e|=\frac{d\text{o }\!\!|\!\!\text{ }}{dt}=B\pi 2r\frac{dr}{dt} $ $ =0.025\times \pi \times 2\times 2\times {{10}^{-2}}\times 1\times {{10}^{-3}} $ $ =\pi \mu V $