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Chapter 17: Problem 33

Suppose a uniform electric field of magnitude \(100.0 \mathrm{N} / \mathrm{C}\) exists in a region of space. How far apart are a pair of equipotential surfaces whose potentials differ by \(1.0 \mathrm{V} ?\)

Short Answer

Expert verified
Answer: The distance between the equipotential surfaces is \(0.01 \mathrm{m}\).

Step by step solution

01

Write down the given values

The electric field \(E = 100.0 \mathrm{N} / \mathrm{C}\) and the potential difference \(\Delta V = 1.0 \mathrm{V}\) are given.
02

Write down the formula for electric field and potential difference

The formula to find the distance between equipotential surfaces is \(E = \frac{\Delta V}{d}\).
03

Rearrange the formula to find the distance

We can rearrange the formula to find the distance between equipotential surfaces as follows: \(d = \frac{\Delta V}{E}\).
04

Substitute the given values into the formula

Now, we can substitute the given values of electric field and potential difference into the formula to find the distance: \(d = \frac{1.0 \mathrm{V}}{100.0 \mathrm{N} / \mathrm{C}}\).
05

Calculate the distance

By dividing the potential difference by the electric field, we find the distance: \(d = \frac{1.0 \mathrm{V}}{100.0 \mathrm{N} / \mathrm{C}} = 0.01 \mathrm{m}\). The equipotential surfaces whose potentials differ by \(1.0 \mathrm{V}\) are \(0.01 \mathrm{m}\) apart.

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Most popular questions from this chapter

In capacitive electrostimulation, electrodes are placed on opposite sides of a limb. A potential difference is applied to the electrodes, which is believed to be beneficial in treating bone defects and breaks. If the capacitance is measured to be \(0.59 \mathrm{pF},\) the electrodes are \(4.0 \mathrm{cm}^{2}\) in area, and the limb is \(3.0 \mathrm{cm}\) in diameter, what is the (average) dielectric constant of the tissue in the limb?
Capacitors are used in many applications where you need to supply a short burst of energy. A \(100.0-\mu \mathrm{F}\) capacitor in an electronic flash lamp supplies an average power of \(10.0 \mathrm{kW}\) to the lamp for $2.0 \mathrm{ms}$. (a) To what potential difference must the capacitor initially be charged? (b) What is its initial charge?
A hydrogen atom has a single proton at its center and a single electron at a distance of approximately \(0.0529 \mathrm{nm}\) from the proton. (a) What is the electric potential energy in joules? (b) What is the significance of the sign of the answer?
Draw some electric field lines and a few equipotential surfaces outside a positively charged conducting cylinder. What shape are the equipotential surfaces?
A spherical conductor of radius \(R\) carries a total charge Q. (a) Show that the magnitude of the electric field just outside the sphere is \(E=\sigma / \epsilon_{0},\) where \(\sigma\) is the charge per unit area on the conductor's surface. (b) Construct an argument to show why the electric field at a point \(P\) just outside any conductor in electrostatic equilibrium has magnitude \(E=\sigma / \epsilon_{0},\) where \(\sigma\) is the local surface charge density. [Hint: Consider a tiny area of an arbitrary conductor and compare it to an area of the same size on a spherical conductor with the same charge density. Think about the number of field lines starting or ending on the two areas.]
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