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Chapter 22: Problem 6

Must the electric field be zero at any point where the potential is zero? Explain.

Short Answer

Expert verified
No, the electric field does not have to be zero at any point where the potential is zero. Zero potential does not imply zero electric field. The electric field is related to the change in electric potential, not the potential itself. Hence there can be an electric field present even if the potential is zero, as long as there is a potential difference or gradient in the vicinity.

Step by step solution

01

Understand the relationship between electric field and potential

Electric field at a point is defined as the force experienced by a unit positive charge placed at that point due to other charges. While electric potential, is the work done in bringing a unit positive charge from infinity to that point.
02

Reasoning on zero electric potential and field

A zero electric potential at a point does not necessarily mean that the electric field at that point is also zero. The electric field is related to the change in electric potential, not the electric potential itself. Therefore, an electric field can be present even if the potential is zero, as long as there is a potential difference or gradient in the electric field.
03

Further clarification

An example of this situation might be along the perpendicular bisector of a dipole. At this location, the electric potential is zero because the contributions from the two equal-magnitude charges cancel each other out, but the electric field is not zero since field vectors from two charges don't cancel each other but add up.

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Most popular questions from this chapter

A sphere of radius \(R\) carries negative charge of magnitude \(Q,\) distributed in a spherically symmetric way. Find an expression for the escape speed for a proton at the sphere's surface-that is, the speed that would enable the proton to escape to arbitrarily large distances starting at the sphere's surface.

You're an automotive engineer working on the ignition system for a new engine. Its spark plugs have center electrodes made from 2.0 -mm-diameter wire. The electrode ends gradually wear to a hemispherical shape, so they behave approximately like charged spheres. Your job is to specify the minimum potential that ensures these plugs will spark in air, neglecting the presence of the second electrode.

The potential at the center of a uniformly charged ring is \(45 \mathrm{kV}\) and \(15 \mathrm{cm}\) along the ring axis the potential is \(33 \mathrm{kV}\). Find the ring's radius and total charge.

The potential at the surface of a 10 -cm-radius sphere is \(4.8 \mathrm{kV}\) What's the sphere's total charge, assuming charge is distributed in a spherically symmetric way?

How much work does it take to move a 50 - \(\mu\) C charge against a 12-V potential difference?
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