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Chapter 17: Q2Q (page 473)

If a negative charge is initially at rest in an electric field, will it move toward a region of higher potential or lower potential? What about a positive charge? How does the potential energy of the charge change in each instance? Explain.

Short Answer

Expert verified

The force on a negative charge is towards the higher potential. So the negative charge will move towards a region of higher potential.

The force on a positive charge is towards the lower potential. So the positive charge moves towards a region of the lower potential.

When the charges move, they gain kinetic energy and lose potential energy. So their potential energy decreases.

Step by step solution

01

Understanding the force on a charged particle in an electric field

In an electric field, the force on a positive charge is along the direction of the electric field, whereas the force on a negative charge is along the opposite side of the electric field. The direction of the electric field is from the higher potential to the lower potential.

02

Evaluation of the motion of a negative charge in an electric field

In an electric field, the force acting on a charged particle is given as:

\(\overrightarrow F = q\overrightarrow E \)

The force and electric field both are vector quantities.

For a negative charge, the force is,

\(\overrightarrow F = - q\overrightarrow E \)

The negative sign indicates that the direction of the force will be opposite to the direction of the electric field. Since the direction of the electric field is always from higher potential to lower potential, the negative charge will move towards a region of higher potential.

03

Evaluation of the motion of a positive charge in an electric field

For a positive charge, the force is,

\(\overrightarrow F = q\overrightarrow E \)

The positive sign indicates that the direction of the force will be the same as the direction of the electric field. Since the direction of the electric field is always from higher potential to lower potential, the positive charge will move towards a region of the lower potential.

04

Evaluation of the change in potential energy

When charges are at rest initially, they have some potential energy. When they start moving in an electric field, they start to gain kinetic energy and lose potential energy. So their potential energy will decrease.

Thus, when the charges move, they gain kinetic energy and lose potential energy. So their potential energy decreases.

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Most popular questions from this chapter

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: (II) A 3500-pF air-gap capacitor is connected to a 32-V battery. If a piece of mica is placed between the plates, how much charge will flow from the battery?

(I) An electron and a proton are \({\bf{0}}{\bf{.53 \times 1}}{{\bf{0}}^{{\bf{ - 10}}}}\;{\bf{m}}\) apart. What is their dipole moment if they are at rest?

(II) How strong is the electric field between the plates of a \({\bf{0}}{\bf{.80}}\;{\bf{\mu F}}\) air-gap capacitor if they are 2.0 mm apart and each has a charge of \({\bf{62}}\;{\bf{\mu C}}\)?

In the dynamic random access memory (DRAM) of a computer, each memory cell contains a capacitor for charge storage. Each of these cells represents a single binary bit value of 鈥�1鈥� when its 35-fF capacitor \(\left( {{\bf{1}}\;{\bf{fF = 1}}{{\bf{0}}^{{\bf{ - 15}}}}\;{\bf{F}}} \right)\) is charged at 1.5 V, or 鈥�0鈥� when uncharged at 0 V.

(a) When fully charged, how many excess electrons are on a cell capacitor鈥檚 negative plate?

(b) After charge has been placed on a cell capacitor鈥檚 plate, it slowly 鈥渓eaks鈥� off at a rate of about \({\bf{0}}{\bf{.30}}\;{\bf{fC/s}}\). How long does it take for the potential difference across this capacitor to decrease by 2.0% from its fully charged value? (Because of this leakage effect, the charge on a DRAM capacitor is 鈥渞efreshed鈥� many times per second.) Note: A DRAM cell is shown in Fig. 21鈥�29.
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