A faraday disc dynamo of radius R=20cm generates 1.2v in o.o8T magnetic field directed perpendicularly to the plane of the disc. What is the frequency of rotation in rpm
To solve this problem, we can use Faraday's law of electromagnetic induction, which states that the induced voltage is proportional to the rate of change of magnetic flux through the loop.
The magnetic flux through the loop is given by the product of the magnetic field (B) and the area (A) of the loop:
Flux = B * A
In this case, the area of the Faraday disc is equal to the area of a circle with radius R:
A = π * R^2
The rate of change of magnetic flux can be calculated by taking the derivative of the magnetic flux with respect to time (t):
d(Flux) / dt = d(B * A) / dt
Since the magnetic field (B) is constant in this problem, we can express this as:
d(Flux) / dt = B * d(A) / dt
The rate of change of area with respect to time can be related to the angular velocity (ω) of the disc:
d(A) / dt = d(π * R^2) / dt = 2πR * dR / dt = 2πR * ω
Substituting this back into the equation for the rate of change of magnetic flux:
d(Flux) / dt = B * (2πR * ω)
Since the induced voltage (V) is proportional to the rate of change of magnetic flux, we can write:
V = k * d(Flux) / dt
Rearranging and substituting the values given in the problem:
V = k * B * (2πR * ω)
1.2V = k * 0.08T * (2π * 0.2m * ω)
Simplifying and solving for ω:
ω = 1.2V / (k * 0.08T * 2π * 0.2m)
ω = 1.2V / (k * 0.08T * 0.4πm)
ω = 15V / (k * T * πm)
The constant k is not given, but we can still determine the frequency of rotation (f) of the disc using the relationship between the angular velocity (ω) and the frequency:
f = ω / (2π)
Therefore, we can calculate the frequency of rotation (f) in rpm by substituting the values and simplifying the given equation:
f = ω / (2π)
f = (15V / (k * T * πm)) / (2π)
f = 15V / (2k * T * m)
Since the value of the constant k is not given, we cannot determine the exact frequency of rotation (f) without it.