A long solenoid is oriented such that its axis is the x-axis, and its center is at the origin of the coordinate system. The solenoid consists of 150 turns of wire per meter and carries a steady current of 15.0 A. The current in the solenoid travels counter-clockwise when viewed from the positive x-axis. Inside the solenoid is a thin circular coil consisting of 30 turns of wire and has a radius of 9.00 cm. The coil is mounted such that its center is also at the origin, and at time t = 0 the plane of the coil is in the yz-plane. The coil rotates about the y-axis (which goes through its diameter) at a constant angular speed of 3.00 rad/s counter-clockwise when viewed from the positive y-axis. What is the emf generated in the coil as a function of time t? Express your answer in units of volts, but do not include units in your expression. For the sign convention, assume the area vector perpendicular to the coil initially points in the +x-direction at t = 0. (Assume t is in seconds.) ε = 0.0203 X What is the magnitude of the magnetic field of a solenoid? Can you write an expression for the flux as a function of the angle between the field and area vector? How does this angle change with time? Can you use this and Faraday's law to write an expression for the emf? Be careful of signs. V
A long solenoid is oriented such that its axis is the x-axis, and its center is at the origin of the coordinate system. The solenoid consists of 150 turns of wire per meter and carries a steady current of 15.0 A. The current in the solenoid travels counter-clockwise when viewed from the positive x-axis. Inside the solenoid is a thin circular coil consisting of 30 turns of wire and has a radius of 9.00 cm. The coil is mounted such that its center is also at the origin, and at time t = 0 the plane of the coil is in the yz-plane. The coil rotates about the y-axis (which goes through its diameter) at a constant angular speed of 3.00 rad/s counter-clockwise when viewed from the positive y-axis. What is the emf generated in the coil as a function of time t? Express your answer in units of volts, but do not include units in your expression. For the sign convention, assume the area vector perpendicular to the coil initially points in the +x-direction at t = 0. (Assume t is in seconds.) ε = 0.0203 X What is the magnitude of the magnetic field of a solenoid? Can you write an expression for the flux as a function of the angle between the field and area vector? How does this angle change with time? Can you use this and Faraday's law to write an expression for the emf? Be careful of signs. V
Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter22: Magnetic Forces And Magnetic Fields
Section: Chapter Questions
Problem 51P
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Transcribed Image Text:A long solenoid is oriented such that its axis is the x-axis, and its center is at the origin of the coordinate system. The solenoid consists of 150 turns
of wire per meter and carries a steady current of 15.0 A. The current in the solenoid travels counter-clockwise when viewed from the positive
x-axis.
Inside the solenoid is a thin circular coil consisting of 30 turns of wire and has a radius of 9.00 cm. The coil is mounted such that its center is also
at the origin, and at time t = 0 the plane of the coil is in the yz-plane. The coil rotates about the y-axis (which goes through its diameter) at a
constant angular speed of 3.00 rad/s counter-clockwise when viewed from the positive y-axis.
What is the emf generated in the coil as a function of time t? Express your answer in units of volts, but do not include units in your expression. For
the sign convention, assume the area vector perpendicular to the coil initially points in the +x-direction at t = 0. (Assume t is in seconds.)
ε = 0.0203
X
What is the magnitude of the magnetic field of a solenoid? Can you write an expression for the flux as a function of the angle between the field and
area vector? How does this angle change with time? Can you use this and Faraday's law to write an expression for the emf? Be careful of signs. V
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