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A conducting circular loop is placed in a uniform magnetic field of 0.04 T with its plane perpendicular to the field. Some how, the radius of the loop starts shrinking at a constant rate of 2 mm/s. Find the induced emf in the loop at an instant when the radius becomes 2 cm solution. |
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Answer» Solution :Let the RADIUS of the loop be r at time t the magnetic flux linked with the loop at this instant is, `phi=AB=pir^2B` The induced emf in the loop at time t, `|epsilon|=(dphi)/(dt)` `=d/(dt)[pir^2B]` `=2pirB(DR)/(dt)` Here B=0.04 T , r=2 cm `=2xx10^(-2)` m `(dr)/(dt)=2 (mm)/s` `=2xx10^(-3)m/s` `=2pixx2xx10^(-2)xx0.04xx2xx10^(-3)` `therefore |epsilon|=0.32pixx10^(-5)V` `therefore |epsilon|=3.2pixx10^(-6)V=3.2pi MUV` |
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