A coil consists of 200turns of wire . Each turns is a square of side d=18cm, and a uniform magnetic field directed perpendicular to the plane of the coil is turned on. If the field changes linearly from 0 to 0.50T in 0.80s, what is the magnitude of the induced emf in the coil while the field is charging
To find the magnitude of the induced emf in the coil while the field is changing, we can use Faraday's law of electromagnetic induction:
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 the magnetic flux
First, let's find the rate of change of the magnetic flux.
The magnetic flux is given by the product of the magnetic field (B) and the area (A) of the coil:
Φ = B * A
Area of one turn of the coil (A) = d^2 = (0.18m)^2 = 0.0324m^2
Total area of the coil = N * A = 200 * 0.0324m^2 = 6.48m^2
Now, let's find the rate of change of the magnetic flux (dΦ/dt).
The magnetic field is changing linearly from 0 to 0.50T in 0.80s.
So, the rate of change can be calculated as:
dΦ/dt = (change in magnetic field) / (time taken)
= (0.50T - 0T) / 0.80s
= 0.50T / 0.80s
= 0.625 T/s
Now, substitute the values into the formula for the induced emf:
emf = -N * dΦ/dt
= -200 * 0.625 T/s
= -125 T/s
Since the emf is a scalar quantity, the magnitude of the induced emf in the coil while the field is charging is:
|emf| = 125 T/s