Question

jack peddles a stationary bicycle. the pedals of the bicycle are attached to a 1000 turn coil of area 0.10 m2. the coil rotates at half a revolution per second and it is placed in a uniform magnetic field of 0.01 t perpendicular to the axis of rotation of the coil. the maximum voltage generated in the coil is

Answer 1

The maximum voltage generated in the coil is 3.14 V.

According to the question, we are provided that a bicycle turns 1000 of the area of 0.10 m2, where the coil rotates half a revolution per second, which is placed in a uniform magnetic field of 0.01 T.

Therefore, no .of turns the coil took, N = 1000

Area of the coil, A= 0.10 m²

Frequency of the system =0.5 revolutions per second

          = 0.5 Hz

The intensity of the Magnetic  field , B =0.01 T

So the Equation we refer to for the calculating the desired  value

  E(ind) = $-db/dt$

                        = -d(NBAcosωt) / dt ​

                               = − NBA d(cosωt) /dt​

                               =  NBAωsinωt

if sinωt=1,

 maximum E(ind)​=  NBAω

Since we know, ω=2πf

Therefore,  (Eind)max ​=  NBA(2πf)

                                         = (1000)(0.01)(0.1)(2π)(0.5)

  (E(ind))max​=  3.14v.

the value for the voltage we got is 3.14 V

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