An elastic conducting material is stretched into a circular loop of 14.7 cm radius. It is placed with its plane perpendicular to a uniform 0.963 T magnetic field. When released, the radius of the loop starts to shrink at an instantaneous rate of 74.5 cm/s. What emf is induced in volts in the loop at that instant?
1 answer
Question:
An elastic conducting material is stretched into a circular loop of 14.7 cm radius. It is placed with its plane perpendicular to a uniform 0.963 T magnetic field. When released, the radius of the loop starts to shrink at an instantaneous rate of 74.5 cm/s. What emf is induced in volts in the loop at that instant?
Answers
Answer: 0.66 VExplanation:GivenMagnetic field, B = 0.963 TInstantaneous rare = 74.5 cm/s = 0.745 m/sradius, r = 14.7 cm = 0.147 mWe will use the formulaemf = dΦ/dtemf = d(BA)/dtemf = d(Bπr²)/dtif B is constant, then we can sayemf = Bπ d(r²)/dt on differentiating, we have,emf = Bπ (2r dr/dt)emf = 2πrB dr/dt substituting each values, we haveemf = 2 * 3.142 * 0.147 * 0.963 * 0.745emf = 0.66 VTherefore, the induced emf in the loop at that instant is 0.66 V
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