Question

You want to use the idea of electromagnetic induction to make the bulb in your small flashlight glow; it glows when the potential difference across it is 1.5 V. You have a small bar magnet and a coil with 100 turns, each with area 3.0

Answer 1

Part A

According to Faraday's law, voltage (V) generated in the ends of a coil with N turns and area A each when the magnetic field B changes in time t is given by:

We have, [Assuming ? sign to be negative sign in order to have reasonable values of magnetic field and coil size. Note: strongest magnetic field ever trapped in a superconductor is only 17.6T]

                                                            [i.e. no. of turns]

                                            [i.e. area of each turns]

    [i.e. change in magnetic field when magnet is moved 0.04 m]

                                                         [i.e. the required voltage to light the bulb]

We start by finding the rate of change in magnetic field () required to generate 1.5 V. Then we will find the speed that is required to produce the required change in magnetic field.

            [we can take A out because A is constant]

But we know, moving the magnet 0.04m in produces 3.8e-2 T . But we need 50 T/s of magnetic field. Hence, using unitary method, the required speed is given by,

Hence, the magnet should be moved at a speed of 53m/s in order to make to bulb light.

Part B

The speed of 53 m/s is equivalent to about 190 km/h, which is extremely high speed and is difficult to produce merely by a person. With the fastest cricket bowling speed of about 161 km/h in the world, I would suggest the speed of 53 m/s is unreasonable, hence B.