Chapter 8: Problem 19

An electromagnetic wave travels in a region of space occupied only by a free electron. Describe the resulting motion of the electron.

Short Answer

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Answer: The motion of a free electron in the presence of an electromagnetic wave is characterized by its acceleration and deceleration along the direction of the oscillating electric field component of the wave, causing it to move back and forth. Factors such as the electron's mass and initial velocity can also influence its overall motion.

Step by step solution

Understand the nature of electromagnetic waves

Electromagnetic waves consist of oscillating electric and magnetic fields, which are perpendicular to the direction of the wave propagation. The most important aspect that influences the motion of the free electron is the oscillating electric field in the wave.

Interaction between the electron and the electric field

When the electric field of the electromagnetic wave interacts with the free electron, it experiences a force due to the electric field, called the electric force. The electric force can be calculated using the formula: F = qE, where q is the charge of the electron and E is the electric field strength.

Describe the motion of the electron in response to the electric force

Since the electric field oscillates, the electric force acting on the electron will also oscillate. This means that the electron will experience an oscillating force, causing it to accelerate and decelerate periodically. Thus, the electron will move back and forth along the direction of the electric field.

Influence of the electron's mass and initial velocity

The motion of the electron may also be influenced by its mass and initial velocity. A more massive electron will require more force to accelerate to the same degree as a less massive one, and if the electron has an initial velocity in the direction of the electric field or opposite to it, it may affect the electron's motion further.

Conclusion

The motion of a free electron in a region of space occupied by an electromagnetic wave can be described by its acceleration and deceleration along the direction of the oscillating electric field component of the wave. Additionally, the mass and initial velocity of the electron can also influence its overall motion.

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An electromagnetic wave travels in a region of space occupied only by a free electron. Describe the resulting motion of the electron.

Short Answer

Step by step solution

Understand the nature of electromagnetic waves

Interaction between the electron and the electric field

Describe the motion of the electron in response to the electric force

Influence of the electron's mass and initial velocity

Conclusion

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