A proton is fired with a speed of 1.0×106 m/s through the parallel-plate capacitor shown in FIGURE P31.29. The capacitor's electric field is E =(1.0×105 V/m, down). How does an experimenter in the proton's frame explain that the proton experiences no force as the charged plates fly by?

Ch 31: Electromagnetic Fields and Waves

Knight Calc - Physics for Scientists and Engineers 5th Edition

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Knight Calc 5th Edition

Ch 31: Electromagnetic Fields and Waves

Problem 29c

Chapter 31, Problem 29c

A proton is fired with a speed of 1.0×10⁶ m/s through the parallel-plate capacitor shown in FIGURE P31.29. The capacitor's electric field is E =(1.0×10⁵ V/m, down). How does an experimenter in the proton's frame explain that the proton experiences no force as the charged plates fly by?

Verified step by step guidance

Step 1: Begin by analyzing the problem in the proton's frame of reference. In this frame, the proton is stationary, and the parallel-plate capacitor appears to move past the proton at a velocity of 1.0×10^6 m/s.

Step 2: Recognize that the moving charged plates generate a magnetic field in addition to the electric field. This magnetic field is a result of the motion of the charges on the plates relative to the proton.

Step 3: Use the principle of relativity to understand that the proton experiences no net force. The electric field (E) exerts a downward force on the proton, but the magnetic field (B) generated by the moving plates exerts an upward force that exactly cancels the electric force.

Step 4: Apply the Lorentz force equation, F = q(E + v × B), to verify the cancellation of forces. In the proton's frame, the velocity (v) of the plates and the magnetic field (B) are such that the magnetic force balances the electric force.

Step 5: Conclude that the experimenter in the proton's frame explains the lack of force on the proton as a result of the perfect balance between the electric and magnetic forces acting on it.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Electric Field

An electric field is a region around a charged particle where other charged particles experience a force. It is represented by electric field lines that indicate the direction and strength of the field. In this scenario, the electric field (E) is directed downward, indicating that a positive charge, like a proton, would typically experience a force in that direction.

Frame of Reference

A frame of reference is a perspective from which measurements and observations are made. In the proton's frame, it is moving with the same velocity as the proton, which means it perceives itself as stationary. This perspective is crucial for understanding why the proton does not experience a force from the electric field as the charged plates pass by.

Lorentz Force

The Lorentz force describes the force experienced by a charged particle moving through an electric and magnetic field. The force is given by the equation F = q(E + v × B), where q is the charge, E is the electric field, v is the velocity, and B is the magnetic field. In this case, since the proton is moving parallel to the electric field and in its own frame of reference, it does not experience a net force.

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Unpolarized light with intensity 350 W/m² passes first through a polarizing filter with its axis vertical, then through a second polarizing filter. It emerges from the second filter with intensity 131 W/m². What is the angle from vertical of the axis of the second polarizing filter?

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Textbook Question

What is the force (magnitude and direction) on the proton in FIGURE P31.28? Give the direction as an angle cw or ccw from vertical.

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Textbook Question

In FIGURE P31.32, a circular loop of radius r travels with speed v along a charged wire having linear charge density λ. The wire is at rest in the laboratory frame, and it passes through the center of the loop. What electric and magnetic fields would an experimenter in the loop's frame calculate at distance r from the current of part c?

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Textbook Question

FIGURE EX31.23 shows a horizontally polarized radio wave of frequency 1.0×10⁶ Hz traveling into the figure. The maximum electric field strength is 1000 V/m. What is the maximum magnetic field strength?

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Textbook Question

A simple series circuit consists of a 150 Ω resistor, a 25 V battery, a switch, and a 2.5 pF parallel-plate capacitor (initially uncharged) with plates 5.0 mm apart. The switch is closed at t = 0 s. Find the electric flux and the displacement current at t = 0.50 ns.

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Textbook Question

An electron travels with $\vec{v} = (5.0 \times 10^{6} \hat{i}) m/s$ through a point in space where $\vec{E} = (2.0 \times 10^{5} \hat{i} - 2.0 \times 10^{5} \hat{j}) V/m$ and $\vec{B} = - 0.10 \hat{k} T$ . What is the force on the electron?

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