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Chapter 21: Problem 5

Eight field lines emerge from a closed surface surrounding an isolated point charge. Would the number of field lines change if a second identical charge were brought to a point just outside the surface? If not, would anything change? Explain.

Short Answer

Expert verified
The number of field lines from a closed surface surrounding an isolated point charge will not change if a second identical charge is brought near the surface. The configuration or direction of the field lines, however, will be altered due to the interaction between the two charges.

Step by step solution

01

Understand Electric Field Lines

Electric field lines represent both the direction and the magnitude of the electric field around a charged particle. The number of field lines depends on the magnitude of the charge and their direction is determined by the nature of the charge, i.e., whether it is positive (outward direction) or negative (inward direction).
02

Analyze the Effect of an Additional Charge

When another charge is placed outside the enclosed surface, it doesn't alter the net charge inside the enclosed surface, thus the number of field lines originating from the surface will remain the same. But it will affect the direction of those electric field lines outside the enclosed surface due to the interaction of the fields from the two charges.
03

Conclusion

In conclusion, the field lines emerging from a closed surface surrounding a charge depend on the charge inside not on the charges outside the surface. Therefore, the number of field lines will not change but their direction can be altered by outside influences.

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Most popular questions from this chapter

An infinitely long rod of radius \(R\) carries a uniform volume charge density \(\rho .\) Show that the electric field strengths outside and inside the rod are given, respectively, by \(E=\rho R^{2} / 2 \epsilon_{0} r\) and \(E=\rho r / 2 \epsilon_{0},\) where \(r\) is the distance from the rod axis. (Although an infinite rod is an impossibility, your answer is a good approximation for the field of a finite rod whose length is much greater than its diameter.)

A \(2.6-\mu \mathrm{C}\) charge is at the center of a cube \(7.5 \mathrm{cm}\) on each side. What's the electric flux through one face of the cube? (Hint: Think about symmetry, and don't do an integral.)

Can electric field lines ever cross? Why or why not?

Why must the electric field be zero inside a conductor in electrostatic equilibrium?

You're sitting inside an uncharged, hollow spherical shell. Suddenly someone dumps a billion coulombs of charge on the shell, distributed uniformly. What happens to the electric field at your location?
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