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.