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A wheel with 8 metallic spokes each 50 cm long is rotated with a speed of 120 rev/min in a plane normal to the horizontal component of the Earth's magnetic field. The Earth's magnetic field at the place is 0.4 G and the angle of dip is 60^(@). Calculate the emf induced between the axle and the rim of the wheel. How will the value of emf be affected if the number of spokes were increased ? |
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Answer» Solution :As per question NUMBER of spokes in wheel n = 8, length of each spoke l = 50 cm = 0.50 m, angular speed `omega = 120rpm = (120)/60 rps = 2 rps = 4pi rad s^(-1)` earth.s magnetic field `B_(E) = 0.4G = 4.0 x 10^(-5)` T andangle of dip `delta = 60^(@)` As the wheel is rotated in a plane normal to the horizontal component `B_(H)` of the earth.s magnetic field, hence emf induced between the axle and the rim of the wheel `varepsilon 1/2B_(H)l^(2)omega = 1/2B_(E) COS delta l^(2)omega=1/2xx4.010^(-5)xxcos60^(@)xx(0.05)^(2)xx4pi = 3.14xx10^(-5)V` The value of emf REMAINS unaffected when there are 8 spokes in the wheel because all the spokes are connected in parallel. |
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