A 1.56 m wire is wound into a coil with a radius of 3.03 cm. If this coil is rotated at 91.9 rpm in a 0.0672 T magnetic field, what is its maximum emf?
To find the maximum emf induced in the coil, we can use the formula for induced emf:
Emf = -N * A * dφ/dt
where:
- Emf is the induced electromotive force
- N is the number of turns in the coil
- A is the area of the coil
- dφ/dt is the rate of change of magnetic flux
First, let's calculate the number of turns in the coil:
Given the total length of wire = 1.56 m
Given radius of the coil = 3.03 cm = 0.0303 m
The circumference of the coil = 2 * π * r = 2 * π * 0.0303 = 0.1900 m
Number of turns, N = total length of wire / circumference of the coil = 1.56 / 0.1900 = 8.21 (approx. 8 turns)
Now, let's calculate the area of the coil:
Area of the coil = π * r^2 = π * (0.0303)^2 = 0.002895 m^2
Next, let's calculate the rate of change of magnetic flux, dφ/dt:
Given that the coil is rotating at 91.9 rpm
Convert rpm to rad/s: 1 rpm = 2π/60 rad/s
Angular velocity, ω = 91.9 * 2π/60 = 9.66 rad/s
Magnetic field, B = 0.0672 T
Rate of change of magnetic flux, dφ/dt = B * A * ω = 0.0672 * 0.002895 * 9.66 = 0.0156 Wb/s
Finally, we can calculate the maximum emf using the formula:
Emf = -N * A * dφ/dt = -8 * 0.002895 * 0.0156 = -0.036 V
Therefore, the maximum emf induced in the coil is 0.036 V.