A flat coil of wire consisting of 56 turns, each with an area of 39 cm^2, is positioned perpendicularly to a uniform magnetic field that increases its magnitude at a constant rate from
3.1 T to 10 T in 5.7 s. If the coil has a total
resistance of 0.56 Ω, what is the magnitude of
the induced current?
Answer in units of A
cosα=1
ℇ=ΔΦ/Δt = N•Δ(B•Acosα)/ Δt=
=N•A•ΔB/Δt
ℇ=I•R
N•A•ΔB/Δt= I•R
I= N•A•ΔB/Δt•R= ...
To find the magnitude of the induced current in the coil, we can use Faraday's law of electromagnetic induction, which states that the induced voltage in a coil is equal to the rate of change of magnetic flux through the coil.
First, let's find the initial and final magnetic flux through the coil.
The magnetic flux through a coil is given by the formula:
Φ = B * A * N,
Where:
Φ is the magnetic flux,
B is the magnetic field strength,
A is the area of each turn of the coil, and
N is the number of turns in the coil.
Given:
B(initial) = 3.1 T,
B(final) = 10 T,
A = 39 cm^2 = 39 * 10^(-4) m^2,
N = 56.
Initial magnetic flux:
Φ(initial) = B(initial) * A * N
Final magnetic flux:
Φ(final) = B(final) * A * N
Now, let's calculate the change in magnetic flux:
ΔΦ = Φ(final) - Φ(initial)
Next, we can calculate the induced voltage using the formula:
V = -N * ΔΦ / Δt
Where:
V is the induced voltage,
N is the number of turns in the coil,
ΔΦ is the change in magnetic flux, and
Δt is the time interval over which the change occurs.
Given:
Δt = 5.7 s
Now, let's calculate the induced voltage:
V = -N * ΔΦ / Δt
Finally, we can find the magnitude of the induced current using Ohm's law:
I = V / R
Where:
I is the magnitude of the induced current, and
R is the total resistance of the coil.
Given:
R = 0.56 Ω
Now, let's calculate the magnitude of the induced current:
I = V / R
By following these steps and plugging in the given values, you should be able to calculate the magnitude of the induced current.