Question

A coil of wire (35.564 cm2 area) can generate a voltage difference when rotated in a magnetic field. If a 452 turn coil is rotated at 94 Hz in a B field of 0.033 T, what is the voltage created ?

Answer 1

Let's write down the variables we know:

A: area; A = 35.564 cm^2 = 35.564*10^-4 m^2 (base unit for length is meter, not centimeter, so all calculations will be done in m)

N: turns; N = 452

f: frequency; f = 94 Hz; from this we know that ω = 2πf = 188π

B: field strength; B = 0.033 T

Let's name some unknown variables now:

V: voltage created; Vmax: maximum voltage created

φ: angle through which the coil is turned, but more importantly, dφ/dt: rate of change of angle; or angular turn rate

From the equation:

φ = ABNcos(ωt),

we can differentiate both sides to get this:

dφ/dt = ABNω*sin(ωt)

Since V = dφ/dt,

V = ABNω*sin(ωt)

Since this value is at its highest when the sin() expression is equal to 1,

Vmax = ABNω, or

Vmax = ABN2πf

Now that we have this equation, we can substitute all the variables we know in the right, then solve for Vmax.

Vmax = 35.564*10^-4*0.033*452*188π

Plugging this into a calculator,

Vmax = 31.331 V