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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

A particle with a charge of \(+5.0 \mu C\) is released from rest at a point on the \(x\) -axis, where \(x=0.10 \mathrm{~m}\). It begins to move as a result of the presence of a \(+9.0-\mu C\) charge that remains fixed at the origin. What is the kinetic energy of the particle at the instant it passes the point \(x=0.20 \mathrm{~m} ?\)

Show that an electron in a one-dimensional electri. cal potential \(V(x)=A x^{2},\) where the constant \(A\) is a positive real number, will execute simple harmonic motion about the origin. What is the period of that motion?

A classroom Van de Graaff generator accumulates a charge of \(1.00 \cdot 10^{-6} \mathrm{C}\) on its spherical conductor, which has a radius of \(10.0 \mathrm{~cm}\) and stands on an insulating column. Neglecting the effects of the generator base or any other objects or fields, find the potential at the surface of the sphere. Assume that the potential is zero at infinity.

A deuterium ion and a tritium ion each have charge \(+e .\) What work is necessary to be done on the deuterium ion in order to bring it within \(10^{-14} \mathrm{~m}\) of the tritium ion? This is the distance within which the two ions can fuse, as a result of strong nuclear interactions that overcome electrostatic repulsion, to produce a helium-5 nucleus. Express the work in electron-volts.

Two point charges are located at two corners of a rectangle, as shown in the figure. a) What is the electric potential at point \(A ?\) b) What is the potential difference between points \(A\) and \(B ?\)
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