Question

What if we were to drop a magnet with the same mass through a copper coil at different heights? Is the greater the height the greater the emf?

In addition, is the integral of Edt depend on the height.

Lab: Faraday's Law

Answer 1

let us suppose that,

Magnet is small with radius far less than the radius of coil .i.e there is no flux leakage out of the coil.

No of turns in the coil = N

Radius of coil = R

Height from which the magnet falls = h

Velocity of the magnet is given by V = (2gh)^1/2

Length of coil = L meters

Time taken by the magnet to cross the coil(T) = L/V seconds

Let us assume that the magnetic field of the magnet has significant value say 'B' Tesla just in front of it. The magnetic field in the coil is zero till the moment just before the magnet enters and from the moment just after the magnet leaves.when the magnet is inside the coil it takes L/V seconds to come out of it.

Magnetic flux when the magnet is inside the coil = BxA weber(Area of coil (A) = ?R²).

d?/dt = (B?R² - 0)÷ T

Applying Faraday's law,

emf induced =

= -NxB?R²V÷L

= -NxB?R²x(2gh)^1/2÷L

Therefore, integral E.dl does depend on height at which coils are situated and is proportional to h^1/2. Hence, greater the height greater the emf.