Induced Electric Fields
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Ampere's Law has shown us how currents, moving electric charges, can create magnetic fields.
Faraday's Law has shown us how changing magnetic fields can induce an emf in a closed loop.
Now we are going to reinterpret Faraday's Law to see how the changing flux induces a nonconservative electric field in a coil.
Let's begin by placing a loop of wire outside of a solenoid whose counterclockwise current is going to be reduced gradually. In the first diagram, no current is induced in the outside loop because the current in the solenoid is steady. Once the current in the solenoid decreases, the magnetic field in the solenoid's core decreases and an emf will be induced in the wire loop.
The force that pushes the charges around the wire is F = qE, where E is the induced electric field. Since this force is parallel to the direction in which the charges are moving, it does work on them as they move around the loop.
Notice that this induced electric field is different from an electrostatic field created by a stationary point charge. When a test charge is moved along any given equipotential surface, no work is done by these conservative fields since the electric force acts perpendicular to the surface. Work can only be done when the force, or a component of the force, acts in the direction of motion. Or equivalently, work is done when the test charge is moved from one equipotential surface (voltage) to another.
Refer to the following information for the next question.
A long solenoid has 3000 turns on its 60-cm length. The inner diameter of the solenoid is 3 cm. As illustrated in this lesson, suppose that a circular loop of radius 4 cm encircles the solenoid.
If the current in the solenoid is decreased at 0.2 A/sec, what is the induced electric field within the wire loop?
Refer to the following information for the next three questions.
Consider an isolated, conducting rod moving perpendicularly through a uniform magnetic field at speed
Calculate the electric field induced in the rod.
What is the direction of this induced electric field?
Calculate the voltage across the ends of the rod.
A Comparison of RC and RL Circuits
A Special Case of Induction
Electricity and Magnetism Background
Generators, Motors, Transformers
Practice with Induced Currents (Changing Areas)
Practice with Induced Currents (Constant Area)
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Catharine H. Colwell
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