Imagine having an 80-turn coil with radius of 5.0 cm and resistance of 30 Ù. At what rate must a perpendicular magnetic field change to produce a current of 4.0 A?

To find the rate at which a perpendicular magnetic field must change to produce a current of 4.0 A in an 80-turn coil with a radius of 5.0 cm and a resistance of 30 Ω, you can use Faraday's law of electromagnetic induction.

Faraday's law states that the induced electromotive force (EMF) in a coil is equal to the rate of change of magnetic flux passing through the coil. Mathematically, it can be written as:

EMF = -N * (dΦ/dt)

Where:
- EMF is the induced electromotive force
- N is the number of turns in the coil
- dΦ/dt is the rate of change of magnetic flux

In this case, we are given that the induced current is 4.0 A. The induced EMF can be calculated using Ohm's law:

EMF = I * R

Where:
- I is the current passing through the coil
- R is the resistance of the coil

Substituting the given values, we have:

EMF = 4.0 A * 30 Ω = 120 V

Since the coil has 80 turns, we can now calculate the rate of change of magnetic flux required to produce this EMF:

(dΦ/dt) = -EMF / N

Substituting the values, we get:

(dΦ/dt) = -120 V / 80 = -1.5 V/turn

Therefore, the rate at which the perpendicular magnetic field must change is -1.5 V/turn. The negative sign indicates that the magnetic field should decrease (or increase in the opposite direction) to induce the current in the coil.