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Chapter 22: Problem 5

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

Short Answer

Expert verified
No, the potential does not need to be zero at a point if the electric field at that point is zero.

Step by step solution

01

Definition of the electric field

The electric field at a point is defined as the electric force experienced by a unit positive charge at that point. It's derived from the primary Coulomb's law. If the electric field is zero, it means there's no net force acting on a unit positive charge at that point.
02

Definition of electric potential

Electric potential at a point is the work done to bring a unit positive charge from infinity to that point against the electric field. If a field is zero at a point, it doesn't mean the work done to bring a charge to that point is also zero. It's rather the force (field) that's zero which means that no work is needed to bring the charge further to that point.
03

Relationship between electric field and potential

While the electric field is a vector quantity, electric potential is scalar. The electric field is the negative gradient of the electric potential. Zero electric field at a point doesn't necessitate that the gradient (change) of potential is also zero at that point, it only means that the potential does not change further from that point.

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Most popular questions from this chapter

The potential on the axis of a uniformly charged disk at \(5.0 \mathrm{cm}\) from the disk center is \(150 \mathrm{V}\); the potential \(10 \mathrm{cm}\) from the disk center is 110 V. Find the disk radius and its total charge.

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.

"Cherry picker" trucks for working on power lines often carry electrocution hazard signs. Explain how this hazard arises and why it might be more of a danger to someone on the ground than to a worker on the truck.

A thin spherical shell has radius \(R\) and total charge \(Q\) distributed uniformly over its surface. Find the potential at its center.

An open-ended cylinder of radius \(a\) and length \(2 a\) carries charge \(q\) spread uniformly over its surface. Find the potential at the center of the cylinder. (Hint: Treat the cylinder as a stack of charged rings, and integrate.)
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