Chapter 18: Electric Charge and Electric Field

Figure shows an electric field extending over three regions, labeled I, II, and III. Answer the following questions. (a) Are there any isolated charges? If so, in what region and what are their signs? (b) Where is the field strongest? (c) Where is it weakest? (d) Where is the field the most uniform?

If two equal charges each of$1\mathrm{C}$each are separated in air by a distance of$1\mathrm{k}\mathrm{m}$, what is the magnitude of the force acting between them? You will see that even at a distance as large as$1\mathrm{k}\mathrm{m}$, the repulsive force is substantial because$1\mathrm{C}$is a very significant amount of charge.

A cell membrane is a thin layer enveloping a cell. The thickness of the membrane is much less than the size of the cell. In a static situation the membrane has a charge distribution of −2.5×10⁻⁶ C/m² on its inner surface and +2.5×10⁻⁶ C/m² on its outer surface. Draw a diagram of the cell and the surrounding cell membrane. Include on this diagram the charge distribution and the corresponding electric field. Is there any electric field inside the cell? Is there any electric field outside the cell?

A test charge of $+2\mu \mathrm{C}$ is placed halfway between a charge of $+6\mu \mathrm{C}$ and another of $+4\mu \mathrm{C}$ separated by $10\mathrm{c}\mathrm{m}$. (a) What is the magnitude of the force on the test charge? (b) What is the direction of this force (away from or toward the $+6\mu \mathrm{C}$charge)?

Is the object in Figure a conductor or an insulator? Justify your answer.

Bare free charges do not remain stationary when close together. To illustrate this, calculate the acceleration of two isolated protons separated by$\mathbf{2}.\mathbf{00}\mathbf{n}\mathbf{m}$(a typical distance between gas atoms). Explicitly show how you follow the steps in the Problem-Solving Strategy for electrostatics.

(a) Two point charges totaling$\mathbf{8}.\mathbf{00}\mu \mathbf{C}$exert a repulsive force of$\mathbf{0}.\mathbf{150}\mathbf{N}$on one another when separated by$\mathbf{0}.\mathbf{500}\mathbf{m}$. What is the charge on each? (b) What is the charge on each if the force is attractive?

(a) Find the total electric field at$x=1.00\mathrm{c}\mathrm{m}$in Figure 18.52(b) given that$q=5.00\mathrm{n}\mathrm{C}$. (b) Find the total electric field at$x=11.00\mathrm{c}\mathrm{m}$in Figure 18.52(b). (c) If the charges are allowed to move and eventually be brought to rest by friction, what will the final charge configuration be? (That is, will there be a single charge, double charge, etc., and what will its value(s) be?)

Figure 18.52 (a) Point charges located at $\mathbf{3}.\mathbf{00},\mathbf{8}.\mathbf{00},\mathbf{a}\mathbf{n}\mathbf{d}\mathbf{11}.\mathbf{0}\mathbf{c}\mathbf{m}$ along the x-axis. (b) Point charges located at $\mathbf{1}.\mathbf{00},\mathbf{5}.\mathbf{00},\mathbf{8}.\mathbf{00},\mathbf{a}\mathbf{n}\mathbf{d}\mathbf{14}.\mathbf{0}\mathbf{c}\mathbf{m}$ along the x-axis

(a) Find the electric field at$x=5.00\mathrm{c}\mathrm{m}$in Figure 18.52 (a), given that$q=1.00\mu C$. (b) At what position between$3.00$and$8.00\mathrm{c}\mathrm{m}$is the total electric field the same as that for$-2q$alone? (c) Can the electric field be zero anywhere between$0.00$and$8.00\mathrm{c}\mathrm{m}$? (d) At very large positive or negative values of$x$, the electric field approaches zero in both (a) and (b). In which does it most rapidly approach zero and why? (e) At what position to the right of$11.0\mathrm{c}\mathrm{m}$is the total electric field zero, other than at infinity? (Hint: A graphing calculator can yield considerable insight in this problem.)

Figure 18.52 (a) Point charges located at$$\mathbf{3}.\mathbf{00},\mathbf{8}.\mathbf{00},\mathbf{a}\mathbf{n}\mathbf{d}\mathbf{11}.\mathbf{0}\mathbf{c}\mathbf{m}$$along the x-axis. (b) Point charges located at$$\mathbf{1}.\mathbf{00},\mathbf{5}.\mathbf{00},\mathbf{8}.\mathbf{00},\mathbf{a}\mathbf{n}\mathbf{d}\mathbf{14}.\mathbf{0}\mathbf{c}\mathbf{m}$$along the x-axis

Using the symmetry of the arrangement, determine the direction of the force on$q$in the figure below, given that$q_a=q_b=+7.50\mu \mathrm{C}$and$q_c=q_d=-7.50\mu \mathrm{C}$. (b) Calculate the magnitude of the force on the charge$q$, given that the square is$10.0\mathrm{c}\mathrm{m}$on a side and$q=2.00\mu \mathrm{C}$.