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Chapter 24: Q. 18 (page 683)

FIGURE $EX 24.18$ shows three charges. Draw these charges on your paper four times. Then draw two-dimensional cross sections of three-dimensional closed surfaces through which the electric flux is (a) $- q / ϵ_{0}$ , (b) $q / ϵ_{0}$ , (c) $3 q / ϵ_{0}$ , and (d) $4 q / ϵ_{0}$ .

Short Answer

Expert verified

a.Diagram for closed surface with charge $- q$ is .

b.Diagram for closed surface with charge $q$ is.

c.Diagram for closed surface with charge $3 q$ is.

d.Diagram for closed surface with charge $4 q$ is.

Step by step solution

01

Figure for closed surface with electric flux -qε0 (part a)

(a).

The amount of electric field that travels through a closed surface is referred to as the electric flux.

$Φ_{e} = \oint \vec{E} \cdot d \vec{A} = \frac{Q_{in}}{ϵ_{o}}$

Because any flux owing to charges outside the closed surface is zero, we construct a closed surface around the number of charges the flux equals to obtain the flux.

Negative charge is surrounded by a closed surfacelocalid="1649268816933" $- q$ .

02

Figure for closed surface with electric flux qε0(part b)

(b).

A closed surface is drawn around net charges of $q$ . If the two charges are combined, this might happen $- q$ and $2 q$ .

03

Figure for closed surface with electric flux 3qε0(part c)

(c).

A closed surface is drawn around net charges of $3 q$ .

This could occur if we combine the three charges $- q$ , $2 q$ and $2 q$ .

04

Figure for closed surface with electric flux 4qε0 (part d)

(d).

A closed surface is drawn around net charges of $4 q$ .

If the two charges $2 q$ and $2 q$ are combined, this might happen.

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Most popular questions from this chapter

$FIGURE P24.48$ shows two very large slabs of metal that are parallel and distance $l$ apart. The top and bottom of each slab has surface area $A$ . The thickness of each slab is so small in comparison to its lateral dimensions that the surface area around the sides is negligible. Metal $1$ has total charge localid="1648838411434" $Q_{1} = Q$ and metal $2$ has total charge localid="1648838418523" $Q_{2} = 2 Q$ . Assume $Q$ is positive. In terms of $Q$ and localid="1648838434998" $A$ , determine a. The electric field strengths localid="1648838424778" $E_{1}$ to localid="1648838441501" $E_{5}$ in regions $1$ to $5$ . b. The surface charge densities localid="1648838447660" $η_{u}$ to localid="1648838454086" $η_{d}$ on the four surfaces $a$ to $d$ .

The cube in FIGURE EX24.6 contains negative charge. The electric field is constant over each face of the cube. Does the missing electric field vector on the front face point in or out? What strength must this field exceed?

The three parallel planes of charge shown in FIGURE $P 24.45$ have surface charge densities $- 12$ , $h$ , $h$ andlocalid="1649410735638" $- 12$ , $h$ - . Find the electric fields localid="1649410752965" $E u 1$ to localid="1649410757308" $E u 4$ in regions localid="1649410763257" $1$ to localid="1649410765846" $4$ .

Suppose you have the uniformly charged cube in FIGURE $Q 24.1$ . Can you use symmetry alone to deduce the shape of the cube’s electric field? If so, sketch and describe the field shape. If not, why not?

A hollow metal sphere has $6 cm$ and $10 cm$ inner and outer radii, respectively. The surface charge density on the inside surface is $- 100 nC / m^{2}$ . The surface charge density on the exterior surface is $+ 100 nC / m^{2}$ . What are the strength and direction of the electric field at points $4$ , $8$ and $12 cm$ from the center?

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