Chapter 24: Gauss’s Law

The square and circle in FIGURE Q24.3 are in the same uniform field. The diameter of the circle equals the edge length of the square. Is ${\Phi }_{square}$larger than, smaller than, or equal to ${\Phi }_{circle}$? Explain.

FIGURE EX24.3 shows a cross section of two infinite parallel planes of charge. Draw this figure on your paper, then draw electric field vectors showing the shape of the electric field.

A tetrahedron has an equilateral triangle base with$20-cm$-long edges and three equilateral triangle sides. The base is parallel to the ground, and a vertical uniform electric field of strength $200N/C$ passes upward through the tetrahedron. a. What is the electric flux through the base? b. What is the electric flux through each of the three sides?

Charges $q_1=-4Q\mathrm{and}{q}_2=+2Q$are located at$x=-a\mathrm{and}x=+a$, respectively. What is the net electric flux through a sphere of radius $2a$centered

(a) at the origin and

(b) at $x=2a$?

A $10nC$charge is at the center of a$2.0m\times 2.0m\times 2.0m$cube. What is the electric flux through the top surface of the cube?

A neutral conductor contains a hollow cavity in which there is a$+100\mathrm{nC}$point charge. A charged rod then transfers$-50\mathrm{nC}$ to the conductor. Afterward, what is the charge (a) on the inner wall of the cavity, and (b) on the exterior surface of the conductor?

A hollow metal sphere has inner radius$\mathrm{a}$and outer radius . The hollow sphere has charge$+2\mathrm{Q}$. A point charge$+\mathrm{Q}$sits at the center of the hollow sphere.

a. Determine the electric fields in the three regions $\mathrm{r}\le \mathrm{a}$,$\mathrm{a}<\mathrm{r}<\mathrm{b}$, and $\mathrm{r}\ge \mathrm{b}$.

b. How much charge is on the inside surface of the hollow sphere$?$On the exterior surface$?$

A $20-\mathrm{cm}$radius ball is uniformly charged to$80\mathrm{nC}$.

a. What is the ball's volume charge density $(\mathrm{C}/{\mathrm{m}}^3)$localid="1648741376835" $?$

b. How much charge is enclosed by spheres of radiilocalid="1648741380973" $5$,localid="1648741279896" $10$andlocalid="1648741787973" $20\mathrm{cm}$localid="1648741405448" $?$

c. What is the electric field strength at points localid="1648741424743" $5$,localid="1648741429590" $10$andlocalid="1648741433205" $20$localid="1648741437392" $\mathrm{cm}$from the centerlocalid="1648741447708" $?$

$\mathrm{FIGURE}\mathrm{P}24.38$shows a solid metal sphere at the center of a hollow metal sphere. What is the total charge on (a) the exterior of the inner sphere, (b) the inside surface of the hollow sphere, and (c) the exterior surface of the hollow sphere?

The earth has a vertical electric field at the surface, pointing down, that averages$100\mathrm{N}/\mathrm{C}$. This field is maintained by various atmospheric processes, including lightning. What is the excess charge on the surface of the earth$?$