The coil has a radius of 8 cm and 110 turns. While moving the magnet farther away from the coil, at a certain point in time, the voltage meter shows -390 mV. What is the magnitude of the rate of change of the flux through the coil?
To find the magnitude of the rate of change of the flux through the coil, we can use Faraday's Law of electromagnetic induction, which states that the induced emf (electromotive force) in a coil is equal to the rate of change of magnetic flux through the coil. The magnetic flux is given by the equation:
Φ = B * A
where Φ is the magnetic flux, B is the magnetic field, and A is the area of the coil.
In this case, we are given the radius of the coil, which means we can calculate the area of the coil using the formula:
A = π * r^2
where A is the area and r is the radius of the coil.
Given that the radius of the coil is 8 cm, we can convert it to meters by dividing it by 100:
r = 8 cm / 100 = 0.08 m
Substituting the value of the radius into the area formula, we get:
A = π * (0.08 m)^2 = 0.0201 m^2 (approximately)
Now, we need to determine the change in flux (dΦ) and the time taken for that change (∆t). We can find the change in flux by multiplying the magnetic field (B) by the area (A) and the number of turns (N) in the coil:
dΦ = B * A * N
Given that the radius of the coil is 8 cm, we can convert it to meters by dividing it by 100:
B = -390 mV
Now, let's solve for the rate of change of the flux (∆Φ/∆t):
∆Φ/∆t = dΦ / ∆t
Here, ∆t is the time taken for the change in the magnetic flux.
Since the problem states that the voltage meter shows -390 mV at a certain point in time, we can assume that ∆t is small or infinitesimal.
Thus, the magnitude of the rate of change of the flux through the coil is given by the absolute value of ∆Φ/∆t.