A copper rod of length L is rotating about midpoint of rod perpendicular to the magnetic field B with constant angular velocity Omega The induced EMF between the two ends is
Answers
Since the copper rod is rotating about its midpoint, so we'll take the midpoint as reference and then considering a differential length of the rod dx from its centre. Since the rod is rotating with an angular velocity w and we're considering a differential area so the angular velocity of the differential area will be w*x placed in a magnetic field B. So integrating for the evaluation of EMF induced in the coil;
Step1: Taking upper limit as the half section of the rod, equals to L/2 and lower limit as -L/2 for the sake of integration.
Step2: Integrating the function B*w*x as a function of x.
emf\ =\ \int_{-L/2}^{L/2}{B*w*x\ dx}
Step3: Simply solving the integration and applying the limits
emf\ =[(BwL^2)/8-(BwL^2)/8]
emf = 0 volts.
Conclusion: When the copper rod of length is rotating perpendicularly in the magnetic field then no emf will induce in the rod.
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