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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 where the electric field is zero. It could be any constant value because the electric field is the negative gradient of potential, meaning that if E is zero, the potential is constant (not necessarily zero).

Step by step solution

01

Understanding Electric Field and Potential

The electric field, E, and the electric potential, V, are related. Specifically, the electric field is the negative gradient of the electric potential. This is mathematically expressed as E = -∇V where ∇ is the gradient operator. This relationship tells us that the electric field points in the direction of greatest decrease of the potential.
02

Understanding 'Zero' condition in both E and V

If the electric field is zero, it would mean that the electric potential does not change, or its gradient is zero. This means that we are at a point of constant electric potential. However, this constant could be any real number, since only the change in electric potential possesses physical significance.
03

Conclude

Even though the electric field E is zero at a certain point, the electric potential V at that point does not necessarily need to be zero. Instead, it could be any constant value, as long as it doesn't change (since E = -∇V and E is zero, ∇V must also be zero).

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Most popular questions from this chapter

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.)

In a uniform electric field, equipotential planes that differ by \(1.0 \mathrm{V}\) are \(2.5 \mathrm{cm}\) apart. What's the field strength?

A 5.0 -g object carries \(3.8 \mu \mathrm{C}\). It acquires speed \(v\) when accelerated from rest through a potential difference \(V\). If a 2.0 -g object acquires twice the speed under the same circumstances, what's its charge?

Find the potential as a function of position in the electric field \(\vec{E}=a x \hat{\imath},\) where \(a\) is a constant and \(V=0\) at \(x=0\)

Two metal spheres each \(1.0 \mathrm{cm}\) in radius are far apart. One sphere carries 38 nC. the other -10 nC. (a) What's the potential on each? (b) If the spheres are connected by a thin wire, what will be the potential on each once equilibrium is reached? (c) How much charge moves between the spheres in order to achieve equilibrium?
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