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Chapter 23: Problem 13

Can two equipotential lines cross? Why or why not?

Short Answer

Expert verified
Why or why not? Answer: No, two equipotential lines cannot cross or intersect each other. This is because each point in a potential field, such as an electric field, can have only one unique potential value, and equipotential lines represent points of equal potential. Intersecting equipotential lines would imply a violation of this basic principle, as a single point would have two different potential values.

Step by step solution

01

Equipotential line definition

Equipotential lines are lines along which the potential (e.g., electric potential) is constant. This means that all points on the line have the same potential value. Since the potential is constant, there is no work done in moving a charge along an equipotential line.
02

Unique potential value per point

In any potential field, each point can have only one unique potential value. Thus, two different equipotential lines cannot have the same value of potential at any given point.
03

Non-intersecting equipotential lines

Since each point in a field can have only one unique potential value, it means that two equipotential lines with different potentials cannot intersect or cross each other at any point. If two equipotential lines were to intersect, it would mean that a point is simultaneously at two different potential values, which is not possible.
04

Conclusion

No, two equipotential lines cannot cross or intersect each other. This is because each point in a potential field, such as an electric field, can have only one unique potential value, and equipotential lines represent points of equal potential. Intersecting equipotential lines would imply a violation of this basic principle, as a single point would have two different potential values.

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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.

Derive an expression for electric potential along the axis (the \(x\) -axis) of a disk with a hole in the center, as shown in the figure, where \(R_{1}\) and \(R_{2}\) are the inner and outer radii of the disk. What would the potential be if \(R_{1}=0 ?\)

An electron moves away from a proton. Describe how the potential it encounters changes. Describe how its potential energy is changing.

Using Gauss's Law and the relation between electric potential and electric field, show that the potential outside a uniformly charged sphere is identical to the potential of a point charge placed at the center of the sphere and equal to the total charge of the sphere. What is the potential at the surface of the sphere? How does the potential change if the charge distribution is not uniform but has spherical (radial) symmetry?

A solid metal ball with a radius of \(3.00 \mathrm{~m}\) has a charge of \(4.00 \mathrm{mC}\). If the electric potential is zero far away from the ball, what is the electric potential at each of the following positions? a) at \(r=0 \mathrm{~m},\) the center of the ball b) at \(r=3.00 \mathrm{~m},\) on the surface of the ball c) at \(r=5.00 \mathrm{~m}\)
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