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Chapter 23: Problem 1

A positive charge is released and moves along an electric field line. This charge moves to a position of a) lower potential and lower potential energy. b) lower potential and higher potential energy. c) higher potential and lower potential energy. d) higher potential and higher potential energy.

Short Answer

Expert verified
a) lower potential and lower potential energy b) lower potential and higher potential energy c) higher potential and higher potential energy d) higher potential and lower potential energy Answer: a) lower potential and lower potential energy

Step by step solution

01

Understanding Electric Potential and Potential Energy

Electric potential is the electric potential energy per unit charge. If a charge moves in the direction of the electric field, the potential decreases. On the other hand, if it moves against the electric field, the potential increases. Electric potential energy is the energy stored in a system as a result of the electrostatic interactions between various charges in the system. The electric potential energy of a charge 'q' at a point in space with potential 'V' is given by U=qV. If the potential decreases, the potential energy also decreases for a positive charge. And, if the potential increases, the potential energy increases for a positive charge.
02

Option (a) Analysis

In this option, both potential and potential energy decrease. Since the charge is positive and moves along the electric field, it would cause the potential to decrease. Also, as the potential decreases, the potential energy of a positive charge would also decrease. So, this option is valid.
03

Option (b) Analysis

In this option, potential decreases, but potential energy increases. This is a contradiction, because if potential decreases for a positive charge, its potential energy should also decrease. So, this option is not valid.
04

Option (c) Analysis

In this option, both potential and potential energy increase. This means that a positive charge would have to move against the electric field, which is not the case stated in the problem (the charge moves along the electric field line). So this option is not valid.
05

Option (d) Analysis

In this option, potential increases, but potential energy decreases. This is a contradiction because if potential increases for a positive charge, its potential energy should also increase. So, this option is not valid. The only valid option is: a) lower potential and lower potential energy.

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Most popular questions from this chapter

Two protons at rest and separated by \(1.00 \mathrm{~mm}\) are released simultaneously. What is the speed of either at the instant when the two are \(10.0 \mathrm{~mm}\) apart?

A charge of \(0.681 \mathrm{nC}\) is placed at \(x=0 .\) Another charge of \(0.167 \mathrm{nC}\) is placed at \(x_{1}=10.9 \mathrm{~cm}\) on the \(x\) -axis. a) What is the combined electrostatic potential of these two charges at \(x=20.1 \mathrm{~cm},\) also on the \(x\) -axis? b) At which point(s) on the \(x\) -axis does this potential have a minimum?

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