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

문제 29c

31장, 문제 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?

검증된 단계별 안내

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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이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.