A closely wound rectangular coil of 80 turns has dimensions of 25 cm by 40 cm. The plane of the coil is rotated from a position where it makes an angle of 37 degrees with a magnetic field of 1.10 T to a position perpendicular to the field. The rotation takes .06 s. What is the average emf induced in the coil?
Divide the magnetic flux change between the two positions by the rotation time interval. Multiply the answer by 80 (the number of turns).
The answer will be in volts.
"Magnetic flux" is the product of the B field and the coil area perpendicular to the field.
The coil area should be in square meters
A closely wound rectangular coil of 80 turns has dimensions of 25 cm by 40 cm. The plane of the coil is rotated from a position where it makes an angle of 37 degrees with a magnetic field of 1.10 T to a position perpendicular to the field. The rotation takes .06 s. What is the average emf induced in the coil?
78
To find the average emf induced in the coil, we can use Faraday's law of electromagnetic induction:
emf = -N * dφ/dt
where:
- emf is the average electromotive force (emf) induced in the coil,
- N is the number of turns in the coil,
- dφ/dt is the rate of change of magnetic flux.
To determine the rate of change of magnetic flux, we need to calculate the initial and final magnetic flux through the coil.
The magnetic flux (Φ) through a coil is given by:
Φ = B * A * cos(θ)
where:
- B is the magnetic field strength,
- A is the area of the coil,
- θ is the angle between the magnetic field and the plane of the coil.
Let's calculate the initial and final flux.
Initial flux (Φi):
B = 1.10 T (given)
A = length * width (25 cm * 40 cm)
θ = 37 degrees (given)
Using the given values, we can calculate the initial flux:
Φi = B * A * cos(θ)
Next, we need to calculate the final flux (Φf) when the coil is perpendicular to the magnetic field. In this case, θ = 90 degrees.
Final flux (Φf) = B * A * cos(90 degrees)
Since cos(90 degrees) = 0, the final flux becomes 0.
Now we have the initial and final flux values required to find the rate of change of magnetic flux.
Rate of change of magnetic flux (dφ/dt) = (Φf - Φi) / Δt
where Δt is the time taken for rotation.
Given that Δt = 0.06 s and Φf = 0, we substitute these values and find:
dφ/dt = -Φi / Δt
Finally, we can use the above calculated dφ/dt and the number of turns (N = 80) to find the average emf:
emf = -N * dφ/dt
Substitute the values and perform the final calculation to determine the average emf induced in the coil.