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Chapter 23: Problem 9

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 \(\begin{array}{ll}\text { c) }-5 \mathrm{C} \text { and }-3 \mathrm{C} & \text { same potential energy. }\end{array}\)

Short Answer

Expert verified
Answer: e) All pairs have the same potential energy.

Step by step solution

01

Calculate potential energy for each pair

To calculate the potential energy for each pair, we will use the formula \(U = k\frac{|q_1q_2|}{d}\), where \(k\) is a constant and can be ignored since we are comparing the values. a) \(U_a = \frac{|(+5C)(+3C)|}{d} = \frac{15C^2}{d}\) d) \(U_d = \frac{|(-5C)(+3C)|}{d} = \frac{15C^2}{d}\) b) \(U_b = \frac{|(+5C)(-3C)|}{d} = \frac{15C^2}{d}\) c) \(U_c = \frac{|(-5C)(-3C)|}{d} = \frac{15C^2}{d}\)
02

Compare potential energies

Comparing the potential energy calculated for all the pairs, we can see that they have the same potential energy, which is \(\frac{15C^2}{d}\). Thus, the answer is: e) All pairs have the same potential energy.

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Most popular questions from this chapter

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.

A proton with a speed of \(1.23 \cdot 10^{4} \mathrm{~m} / \mathrm{s}\) is moving from infinity directly toward a second proton. Assuming that the second proton is fixed in place, find the position where the moving proton stops momentarily before turning around.

A spherical water drop \(50.0 \mu \mathrm{m}\) in diameter has a uniformly distributed charge of \(+20.0 \mathrm{pC}\). Find (a) the potential at its surface and (b) the potential at its center.

In which situation is the electric potential the highest? a) at a point \(1 \mathrm{~m}\) from a point charge of \(1 \mathrm{C}\) b) at a point \(1 \mathrm{~m}\) from the center of a uniformly charged spherical shell of radius \(0.5 \mathrm{~m}\) with a total charge of \(1 \mathrm{C}\) c) at a point \(1 \mathrm{~m}\) from the center of a uniformly charged rod of length \(1 \mathrm{~m}\) and with a total charge of \(1 \mathrm{C}\) d) at a point \(2 \mathrm{~m}\) from a point charge of \(2 \mathrm{C}\) e) at a point \(0.5 \mathrm{~m}\) from a point charge of \(0.5 \mathrm{C}\)

An electric field is established in a nonuniform rod. A voltmeter is used to measure the potential difference between the left end of the rod and a point a distance \(x\) from the left end. The process is repeated, and it is found that the data are described by the relationship \(\Delta V=270 x^{2},\) where \(\Delta V\) has the units \(\mathrm{V} / \mathrm{m}^{2}\). What is the \(x\) -component of the electric field at a point \(13 \mathrm{~cm}\) from the left end?
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