Problem 10 A coil of wire has a large alter... [FREE SOLUTION]

Chapter 8: Problem 10

A coil of wire has a large alternating current flowing in it. A piece of aluminum or copper placed near the coil becomes warm even if it does not touch the coil. Explain why.

Short Answer

Expert verified

Answer: The piece of aluminum or copper becomes warm due to electromagnetic induction. The large alternating current in the coil creates a varying magnetic field, which induces an electromotive force (EMF) in the nearby piece of metal, causing an electric current to flow in it. This induced current encounters resistance, resulting in energy being dissipated as heat, thereby, warming the metal piece without direct contact with the coil.

Step by step solution

Describe alternating current in the coil

An alternating current is a current that changes its direction periodically. In a coil with a large alternating current, the electric current flowing through the coil changes its direction at a certain frequency. This change in current direction creates a varying magnetic field around the coil.

Explain electromagnetic induction

According to Faraday's Law of Electromagnetic induction, a change in the magnetic field around a conductor (such as aluminum or copper) induces an electromotive force (EMF) in the conductor. In other words, a changing magnetic field generates an electric current in a nearby conductor.

Apply electromagnetic induction to the situation

In this case, the varying magnetic field created by the alternating current in the coil induces an electromotive force (EMF) in the aluminum or copper piece placed near the coil, which causes an electric current to flow in the piece.

Explain energy transformation

When an electric current flows through a conductor, it encounters some resistance. According to Joule's Law, the energy dissipated in the form of heat due to this resistance is given by the formula: \[P = I^2 R \] where P is the power (in watts) dissipated as heat, I is the current (in amperes) flowing through the conductor, and R is the resistance (in ohms) of the conductor.

Explain the warming effect

In our situation, the induced current in the aluminum or copper piece encounters resistance and, as a result, energy is dissipated as heat. This heat causes the piece to become warm, even without direct contact with the coil. This warming effect is due to the energy transformation from the electromagnetic energy of the coil's varying magnetic field into thermal energy in the aluminum or copper piece.

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91影视

A coil of wire has a large alternating current flowing in it. A piece of aluminum or copper placed near the coil becomes warm even if it does not touch the coil. Explain why.

Short Answer

Step by step solution

Describe alternating current in the coil

Explain electromagnetic induction

Apply electromagnetic induction to the situation

Explain energy transformation

Explain the warming effect

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