How does the graph loook for a magneti?

Question

When a magnet passes through a coil o fiwre, (with the north pole of the magnetc moving towards the coil) how wil the emf induced in the coil look like when the magnetc passes through the coil ...actually going gthrough or inside o f the coils. and then leaving the coil?

Answer 1

Let r = radius of the coil,
L = length of the magnet,
x = x coordinate of the N pole, and
0 = x-coordinate of the coil.
Φ = k/(x^2 + r^2) - k/((x - L)^2 + r^2)
dΦ/dt = [-2kx/(x^2 + r^2)^2 + 2kx/((x - L)^2 + r^2)^2]dx/dt ~ emf

If the velocity of the magnet is constant, the graph of Kx[1/((x - L)^2 + r^2)^2 - 1/(x^2 + r^2)^2] will have the shape of the graph you want. Choose K large enough to get good resolution.