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Chapter 17: Q1Q (page 473)

If two points are at the same potential, does this mean that no net work is done in moving a test charge from one point to the other? Does this imply that no force must be exerted? Explain.

Short Answer

Expert verified

The net work in moving a test charge is zero from one point to another, having the same potential. As the wok is zero, then the force required to move the charge is zero.

Step by step solution

01

Understanding the electric potential

The electric potential energy per unit charge at any point in space is defined as the electric potential at that point.

The expression for electric potential is given as:

\(V = \frac{{PE}}{q}\) 鈥� (i)

Here, V is the electric potential, PE is the potential energy and q is the charge.

02

Evaluation of the work done and force exerted

The potential difference between the two points is given as:

\({V_2} - {V_1} = \frac{{P{E_2} - P{E_1}}}{q}\)

This change in potential energy will be equal to the negative of work done by the electric field in moving the charge.

\(\begin{aligned}{c}{V_2} - {V_1} &= - \frac{W}{q}\\W &= q\left( {{V_2} - {V_1}} \right)\end{aligned}\)

Since both the points are at the same potential, then \({V_2} - {V_1} = 0\).

Therefore,

\(\begin{aligned}{c}W &= q\left( 0 \right)\\W &= 0\end{aligned}\)

Thus, the net work in moving a test charge is zero from one point to another, having the same potential.

Since the wok is zero, then to move the charge, the required force is zero.

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Most popular questions from this chapter

A dielectric is pulled out from between the plates of a capacitor which remains connected to a battery. What changes occur to (a) the capacitance, (b) the charge on the plates, (c) the potential difference, (d) the energy stored in the capacitor, and (e) the electric field? Explain your answers.

Question: Near the surface of the Earth there is an electric field of about \({\bf{150}}\;{{\bf{V}} \mathord{\left/{\vphantom {{\bf{V}} {\bf{m}}}} \right.} {\bf{m}}}\)which points downward. Two identical balls with mass \({\bf{m = 0}}{\bf{.670}}\;{\bf{kg}}\) are dropped from a height of 2.00 m, but one of the balls is positively charged with \({{\bf{q}}_{\bf{1}}}{\bf{ = 650}}\;{\bf{\mu C}}\), and the second is negatively charged with \({{\bf{q}}_{\bf{2}}}{\bf{ = }} - {\bf{650}}\;{\bf{\mu C}}\). Use conservation of energy to determine the difference in the speed of the two balls when they hit the ground. (Neglect air resistance.)

Which of the following statements is valid?

(a) If the potential at a particular point is zero, the field at that point must be zero.

(b) If the field at a particular point is zero, the potential at that point must be zero.

(c) If the field throughout a particular region is constant, the potential throughout that region must be zero.

(d) If the potential throughout a particular region is constant, the field throughout that region must be zero.

Question:An electron is accelerated horizontally from rest by a potential difference of 2200 V. It then passes between two horizontal plates 6.5 cm long and 1.3 cm apart that have a potential difference of 250 V (Fig. 17鈥�50). At what angle\(\theta \)will the electron be traveling after it passes between the plates?

(I) An 8500-pF capacitor holds plus and minus charges of \({\bf{16}}{\bf{.5 \times 1}}{{\bf{0}}^{{\bf{ - 8}}}}\;{\bf{C}}\). What is the voltage across the capacitor?
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