Question

Induced voltage from a generator A coil of wire has N = 500 turns (not all shown in the diagram!) and a radius R =10.0 cm. It is rotated at a rate f = 55 Hz in a constant magnetic field of strength B = 0.015 ?. a) Assume the plane of the coil is at 90° to the direction of the magnetic field lines at t = 0, as shown in the diagram. Write an expression for the time dependence of the angle \(\theta(t)\), in radians, between the directed surface element dA and the magnetic field B. b) Write an expression for the time dependence of the magnetic flux \(\Phi_B\) through the coil. c) Write an expression for the time dependence of the induced EMF, \(\epsilon(t)\) in the coil. d) What is the maximum value (a numerical value in Volts) \(\epsilon_0\) of the induced EMF in the coil? e) Does the induced EMF cause a clockwise or counterclockwise current in the coil, as viewed from the right, when it is at the position shown in the diagram? f) Find an expression for the root-mean-square (rms) value \(\epsilon_{rms}\) of the induced voltage in the coil in terms of \(\epsilon_0\). Find the average value over one revolution of the coil of the square of the induced EMF you found in c). Then find the time average of this by taking its time integral over one cycle, and dividing the result by the time (the period) taken by one cycle. The rms induced voltage is the square root of the result. g) What is the numerical value of \(\epsilon_{rms}\)? h) How many turns N would be required to provide an rms voltage of 120 V, like that of the electrical connections in wall sockets in North American buildings?

          Induced voltage from a generator
A coil of wire has N = 500 turns (not all shown in the diagram!)
and a radius R =10.0 cm. It is rotated at a rate f = 55 Hz in a
constant magnetic field of strength B = 0.015 ?.
a) Assume the plane of the coil is at 90° to the direction of
the magnetic field lines at t = 0, as shown in the diagram.
Write an expression for the time dependence of the angle
\(\theta(t)\), in radians, between the directed surface element dA
and the magnetic field B.
b) Write an expression for the time dependence of the magnetic flux \(\Phi_B\) through the coil.
c) Write an expression for the time dependence of the induced EMF, \(\epsilon(t)\) in the coil.
d) What is the maximum value (a numerical value in Volts) \(\epsilon_0\) of the induced EMF in the coil?
e) Does the induced EMF cause a clockwise or counterclockwise current in the coil, as
viewed from the right, when it is at the position shown in the diagram?
f) Find an expression for the root-mean-square (rms) value \(\epsilon_{rms}\) of the induced voltage in the
coil in terms of \(\epsilon_0\).
Find the average value over one revolution of the coil of the square of the induced EMF you
found in c). Then find the time average of this by taking its time integral over one cycle, and
dividing the result by the time (the period) taken by one cycle. The rms induced voltage is
the square root of the result.
g) What is the numerical value of \(\epsilon_{rms}\)?
h) How many turns N would be required to provide an rms voltage of 120 V, like that of the
electrical connections in wall sockets in North American buildings?

Induced voltage from a generator
A coil of wire has N = 500 turns (not all shown in the diagram!)
and a radius R =10.0 cm. It is rotated at a rate f = 55 Hz in a
constant magnetic field of strength B = 0.015 ?.
a) Assume the plane of the coil is at 90° to the direction of
the magnetic field lines at t = 0, as shown in the diagram.
Write an expression for the time dependence of the angle
θ(t), in radians, between the directed surface element dA
and the magnetic field B.
b) Write an expression for the time dependence of the magnetic flux through the coil.
c) Write an expression for the time dependence of the induced EMF, ϵ(t) in the coil.
d) What is the maximum value (a numerical value in Volts) ϵ0 of the induced EMF in the coil?
e) Does the induced EMF cause a clockwise or counterclockwise current in the coil, as
viewed from the right, when it is at the position shown in the diagram?
f) Find an expression for the root-mean-square (rms) value ϵrms of the induced voltage in the
coil in terms of ϵ0.
Find the average value over one revolution of the coil of the square of the induced EMF you
found in c). Then find the time average of this by taking its time integral over one cycle, and
dividing the result by the time (the period) taken by one cycle. The rms induced voltage is
the square root of the result.
g) What is the numerical value of ϵrms?
h) How many turns N would be required to provide an rms voltage of 120 V, like that of the
electrical connections in wall sockets in North American buildings?

Added by Dennis G.

Question

Please give Ace some feedback