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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

A point charge \(Q\) is placed a distance \(R\) from the center of a conducting sphere of radius \(a,\) with \(R>a\) (the point charge is outside the sphere). The sphere is grounded, that is, connected to a distant, unlimited source and/or sink of charge at zero potential. (Neither the distant ground nor the connection directly affects the electric field in the vicinity of the charge and sphere.) As a result, the sphere acquires a charge opposite in sign to \(Q\), and the point charge experiences an attractive force toward the sphere. a) Remarkably, the electric field outside the sphere is the same as would be produced by the point charge \(Q\) plus an imaginary mirror-image point charge \(q\), with magnitude and location that make the set of points corresponding to the surface of the sphere an equipotential of potential zero. That is, the imaginary point charge produces the same field contribution outside the sphere as the actual surface charge on the sphere. Calculate the value and location of \(q\). (Hint: By symmetry, \(q\) must lie somewhere on the axis that passes through the center of the sphere and the location of \(Q .)\) b) Calculate the force exerted on point charge \(Q\) and directed toward the sphere, in terms of the original quantities \(Q, R,\) and \(a\) c) Determine the actual nonuniform surface charge distribution on the conducting sphere.

Consider an electron in the ground state of the hydrogen atom, separated from the proton by a distance of \(0.0529 \mathrm{nm}\) a) Viewing the electron as a satellite orbiting the proton in the electrostatic potential, calculate the speed of the electron in its orbit. b) Calculate an effective escape speed for the electron. c) Calculate the energy of an electron having this speed, and from it determine the energy that must be given to the electron to ionize the hydrogen atom.

Fully stripped (all electrons removed) sulfur \(\left({ }^{32} \mathrm{~S}\right)\) ions are accelerated in an accelerator from rest using a total voltage of \(1.00 \cdot 10^{9} \mathrm{~V}\). \({ }^{32} \mathrm{~S}\) has 16 protons and 16 neutrons. The accelerator produces a beam consisting of \(6.61 \cdot 10^{12}\) ions per second. This beam of ions is completely stopped in a beam dump. What is the total power the beam dump has to absorb?

A charge \(Q=\) \(+5.60 \mu C\) is uniformly distributed on a thin cylindrical plastic shell. The radius, \(R\), of the shell is \(4.50 \mathrm{~cm}\). Calculate the electric potential at the origin of the \(x y\) -coordinate system shown in the figure. Assume that the electric potential is zero at points infinitely far away from the origin.

Two fixed point charges are on the \(x\) -axis. A charge of \(-3.00 \mathrm{mC}\) is located at \(x=+2.00 \mathrm{~m}\) and a charge of \(+5.00 \mathrm{mC}\) is located at \(x=-4.00 \mathrm{~m}\) a) Find the electric potential, \(V(x),\) for an arbitrary point on the \(x\) -axis. b) At what position(s) on the \(x\) -axis is \(V(x)=0 ?\) c) Find \(E(x)\) for an arbitrary point on the \(x\) -axis.
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