Question

a metal disc is made up to spin at 20 revolution per second about an axis passig through its centre and normal to its plane the disc has a radius of 30 cm and spins in a uniform magnetic field of 0.20 T. Which is parallel to the axis of rotation. Calculate
a) the area swept out per second by the radius of the disc
b) the Flux cut per second by the radius of the disc
C) the induced emf in the disc​

Answer 1

Explanation:

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Answer 2

Given info : A metal disc is made up to spin at 20 rev/s about an axis passing through its centre and normal to its plane. radius of disc is 30cm and spins in a uniform magnetic field of 0.2 T which is parallel to the axis of rotation.

To find :

1. The area swept out per second by the radius of the disc.
2. the flux cut per second by the radius of the disc
3. The induced emf in the disc.

solution : frequency = ω/2π

= (20 rev/s)/2π

= (20 × 2π rad/s)/2π

= 20 /sec or 20 Hz

1. The area swept out per second by the radius of the disc = frequency × area of disc

= 20 × πr²

= 20 × 3.14 × (30 × 10^-2)²

= 62.8 × 0.09 m²/s

= 5.652 m²/s

2. The flux cut out per second by the radius of the disc = dΦ/dt

= d(BA)/dt

= B dA/dt

= Bf

= 0.2 T × 5.652 m²/s

= 1.131 Wb/s

3. The magnitude of induced emf = rate of change of magnetic flux = 1.131 wb/s = 1.131 Volts