What is the strength of the electric field in a region where the electric potential is constant?

Short Answer

Expert verified

The electric field’s strength will be zero in a region with constant electric potential.

Step by step solution

01

Definition of the electric field

The change in potential with respect to the position gives the electric field strength. Its direction is opposite to the potential gradient.

\(E = - \frac{{dV}}{{dx}}\)

02

calculating the electric field’s strength in a region with constant electric potential

In the region where electric potential is constant, the change in potential with respect to the position is zero.

That means the electric field strength will be zero.

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Most popular questions from this chapter

Integrated Concepts

A \(12.0\;V\)battery-operated bottle warmer heats \(50.0\;g\)of glass, \(2.50 \times {10^2}{\rm{ }}g\)of baby formula, and \(2.00 \times {10^2}\;g\)of aluminium from \({20.0^\circ }C\) to \({90.0^\circ }C\).

(a) How much charge is moved by the battery?

(b) How many electrons per second flow if it takes \(5.00\)min to warm the formula? (Hint: Assume that the specific heat of baby formula is about the same as the specific heat of water.)

(a) What is the potential between two points situated \(10{\rm{ }}cm\) and \(20{\rm{ }}cm\) from a \(3.0{\rm{ }}\mu C\) point charge? (b) To what location should the point at \(20{\rm{ }}cm\) be moved to increase this potential difference by a factor of two?

The naturally occurring charge on the ground on a fine day out in the open country is \( - 1.00n{\rm{ }}C/{m^2}\).

(a) What is the electric field relative to ground at a height of \(3.00{\rm{ }}m\)?

(b) Calculate the electric potential at this height.

(c) Sketch electric field and equipotential lines for this scenario.

Which methods of radiation protection were used in the device shown in the first photo in Figure 32.35? Which were used in the situation shown in the second photo?

Figure 32.35 (a)

Figure 32.35(b)

(a) This x-ray fluorescence machine is one of the thousands used in shoe stores to produce images of feet as a check on the fit of shoes. They are unshielded and remain on as long as the feet are in them, producing doses much greater than medical images. Children were fascinated with them. These machines were used in shoe stores until laws preventing such unwarranted radiation exposure were enacted in the 1950s. (credit: Andrew Kuchling ) (b) Now that we know the effects of exposure to radioactive material, safety is a priority. (credit: U.S. Navy)

If the voltage between two points is zero, can a test charge be moved between them with zero net work being done? Can this necessarily be done without exerting a force? Explain.

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