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Chapter 23: Problem 23

How much work would be done by an electric field in moving a proton from a point at a potential of \(+180 . \mathrm{V}\) to a point at a potential of \(-60.0 \mathrm{~V} ?\)

Short Answer

Expert verified
Question: Calculate the work done by an electric field in moving a proton from a point at a potential of +180 V to a point at a potential of -60 V. Answer: The work done by the electric field is \(3.84\times 10^{-17}\) J.

Step by step solution

01

Identify the given values

In this problem, we have the following given values: - Potential at the initial point (V1): \(+180\) V - Potential at the final point (V2): \(-60\) V - Charge of a proton (q): \(+1.6\times10^{-19}\) C
02

Calculate the potential difference

To find the potential difference, subtract the final potential (V2) from the initial potential (V1): \(\Delta V = V_1 - V_2 = (+180) - (-60) = 240\) V
03

Calculate the work done

Now use the formula \(W = q\Delta V\) to find the work done by the electric field in moving the proton: \(W = (1.6\times10^{-19}\,\text{C})(240\,\text{V}) = 3.84 \times 10^{-17}\,\text{J}\)
04

Write the final answer

The work done by the electric field in moving a proton from a point at a potential of \(+180\) V to a point at a potential of \(-60\) V is \(3.84\times 10^{-17}\) J.

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Most popular questions from this chapter

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.

Each of the following pairs of charges are separated by a distance \(d\). Which pair has the highest potential energy? a) \(+5 \mathrm{C}\) and \(+3 \mathrm{C}\) d) \(-5 \mathrm{C}\) and \(+3 \mathrm{C}\) b) \(+5 \mathrm{C}\) and \(-3 \mathrm{C}\) e) All pairs have the \(\begin{array}{ll}\text { c) }-5 \mathrm{C} \text { and }-3 \mathrm{C} & \text { same potential energy. }\end{array}\)

Can two equipotential lines cross? Why or why not?

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

Two metal spheres of radii \(r_{1}=10.0 \mathrm{~cm}\) and \(r_{2}=\) \(20.0 \mathrm{~cm},\) respectively, have been positively charged so that both have a total charge of \(100, \mu C\) a) What is the ratio of their surface charge distributions? b) If the two spheres are connected by a copper wire, how much charge flows through the wire before the system reaches equilibrium?
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