A coil with an area of 0.10 m2 is in a magnetic field of 0.20 T perpendicular to its area. It is flipped through 180° so that the part that was up is down. The flip takes 1.0 s. Estimate the average induced emf between the ends of the coil while it is being flipped.
What formula?
ε = - ΔΦ/ Δt = -( Φ(max) –(- Φ(max))/ Δt=
=-2 Φ(max)/ Δt =- 2•B•A/ Δt =
= -2•0.2•0.1/1 = 0.04 V
The formula that relates the average induced electromotive force (emf) to the change in magnetic flux is:
emf = -N(dϕ/dt)
Where:
- emf is the induced electromotive force (measured in volts)
- N is the number of turns in the coil
- dϕ/dt is the rate of change of magnetic flux (measured in webers per second)
In this scenario, the coil is flipped through 180°, so the change in magnetic flux can be calculated by finding the initial and final magnetic flux and taking their difference.
To estimate the average induced emf in the coil while it is being flipped, we can use Faraday's law of electromagnetic induction. The formula for calculating the induced emf is given by:
emf = -N * (dΦ/dt)
Where:
emf = induced electromotive force (in volts)
N = number of turns in the coil
dΦ/dt = rate of change of magnetic flux
In this case, the coil is flipped through 180°, which means there is a change in magnetic flux. The magnetic flux (Φ) through the coil is given by:
Φ = B * A
Where:
B = magnetic field strength (in teslas)
A = area of the coil (in square meters)
Let's plug in the given values into the formulas to calculate the average induced emf.
emf = -N * (dΦ/dt)
We are given:
B = 0.20 T (teslas)
A = 0.10 m^2 (square meters)
N is not given, so we'll assume it as 1 for simplicity.
The flip takes 1.0 s.
Firstly, we need to calculate the change in magnetic flux (dΦ) during the flip. The initial magnetic flux is given by:
Φ_initial = B * A
The final magnetic flux after the flip is given by:
Φ_final = -B * A
Now we can calculate the change in magnetic flux:
dΦ = Φ_final - Φ_initial
Next, we can calculate the average induced emf:
emf = -N * (dΦ/dt)
Substituting the values, we get:
emf = -1 * [(Φ_final - Φ_initial) / (time taken for the flip)]
emf = -1 * [(-B * A - B * A) / 1.0 s]
emf = -2 * B * A / 1.0 s
emf = -2 * 0.20 T * 0.10 m^2 / 1.0 s
emf = -0.04 V
Therefore, the estimated average induced emf between the ends of the coil while it is being flipped is approximately -0.04 V.