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Chapter 23: Problem 2

A proton is placed midway between points \(A\) and \(B\). The potential at point \(A\) is \(-20 \mathrm{~V}\), and the potential at point \(B\) \(+20 \mathrm{~V}\). The potential at the midpoint is \(0 \mathrm{~V}\). The proton will a) remain at rest. b) move toward point \(B\) with constant velocity. c) accelerate toward point \(A\). d) accelerate toward point \(B\). e) move toward point \(A\) with constant velocity.

Short Answer

Expert verified
Answer: c) accelerate toward point A

Step by step solution

01

Define the electric potential values

Point A has an electric potential of \(-20 V\), while point B has an electric potential of \(+20 V\). The proton is placed midway between these points, where the electric potential is \(0 V\).
02

Determine the electric field direction

The presence of electric potential between points A and B indicates that there is an electric field between them. The electric field lines move from high potential to low potential. In this case, it means that the electric field points from point B towards point A.
03

Identify the electric force acting on the proton

A proton is a positively charged particle. In an electric field, its motion will be determined by the electric force acting on it. Since the electric field goes from point B to point A (from high to low potential), the electric force on the proton will follow the same direction. The proton will, therefore, be attracted towards point A.
04

Check the given options according to the determined behavior of the proton

Based on the electric force, we can rule out options a), b), and e), as the proton will not remain at rest, and will not move towards point B in any way. The remaining options are c) accelerate toward point A and d) accelerate toward point B.
05

Determine whether the proton accelerates or moves with a constant velocity

The electric field between points A and B remains constant throughout (since the potential difference of \(\pm20 V\) doesn't change). This constant electric field means that a constant electric force will act on the proton. According to Newton's second law, a constant force acting on a particle causes it to accelerate in the direction of the force. Therefore, the proton will accelerate.
06

Select the correct option based on the proton's behavior

Based on our analysis, the proton will accelerate towards point A due to the electric force acting on it. The correct answer is: c) accelerate toward point A.

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Most popular questions from this chapter

An electron is accelerated from rest through a potential difference of \(370 \mathrm{~V}\). What is its final speed?

A hollow spherical conductor with a \(5.0-\mathrm{cm}\) radius has a surface charge of \(8.0 \mathrm{nC}\). a) What is the potential \(8.0 \mathrm{~cm}\) from the center of the sphere? b) What is the potential \(3.0 \mathrm{~cm}\) from the center of the sphere? c) What is the potential at the center of the sphere?

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What potential difference is needed to give an alpha particle (composed of 2 protons and 2 neutrons) \(200 \mathrm{keV}\) of kinetic energy?

One of the greatest physics experiments in history measured the charge-to-mass ratio of an electron, \(q / m .\) If a uniform potential difference is created between two plates, atomized particles - each with an integral amount of charge-can be suspended in space. The assumption is that the particles of unknown mass, \(M,\) contain a net number, \(n\), of electrons of mass \(m\) and charge \(q .\) For a plate separation of \(d,\) what is the potential difference necessary to suspend a particle of mass \(M\) containing \(n\) net electrons? What is the acceleration of the particle if the voltage is cut in half? What is the acceleration of the particle if the voltage is doubled?
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