Question

A rectangular coil with N turns and area A is place in a uniform magnetic field directed into y-direction. (a) What amount of emf is induced in the coil if the coil doesn’t move or rotate? . Let’s say the coil rotates about the z-axis through its center at a constant angular velocity LaTeX: \omegaω. (b) What would be total magnetic flux through the coil as a function of LaTeX: \thetaθ ? (LaTeX: \thetaθ is the angle between the directions of area A and field-B) (c) Now, what amount of emf will be induced when the coil is rotating? (d) Is the magnitude of this emf time independent? If not show quantitatively and explain how it change with time. (e) Will it have a "rms Voltage" associated with it? If so what would be its "rms Voltage"?

Answer 1

1) emf induced when the coil does not rotate = 0 volts ( it is so because , according to the faraday's law , the emf induced is equal to the rate of change of magnetic flux through a loop).

2) total magnetic flux = N*B*A*cos()

where N is the number of turns

B is the magnetic flux

A is the area

is the angle between the magnetic field and area vector of loop.

3) emf induced = rate of change of magnetic flux

= d( N*B*A*cos(wt))/dt

= - N*B*A*w*sin(wt)

negative sign simply shows the direction of induced emf

4) no, the magnitude of emf is not independent of time.it is so because teh experession of induced emf = N*B*A*w*sin(wt) ; which involves a factor of "t" in the SINE of angle.

5) the rms voltage = (1/ )times the peak voltage

= N*B*A*w/