5.5 Calculating Electric Fields of Charge Distributions

Line, surface, and volume charge densities, and setting up integrals for rods, rings, disks, and sheets where summation over points fails.

University Physics Volume 2, 5.5 Calculating Electric Fields of Charge Distributions

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11 exercises

5.5 Exercise 1

How would the strategy used above change to calculate the electric field at a point a distance z above one end of the finite line segment?

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5.5 Exercise 2

How would the above limit change with a uniformly charged rectangle instead of a disk?

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5.5 Exercise 3

What would the electric field look like in a system with two parallel positively charged planes with equal charge densities?

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5.5 Exercise 4

Give a plausible argument as to why the electric field outside an infinite charged sheet is constant.

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5.5 Exercise 6

Describe the electric fields of an infinite charged plate and of two infinite, charged parallel plates in terms of the electric field of an infinite sheet of charge.

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5.5 Exercise 9

Calculate the magnitude and direction of the electric field 2.0 m from a long wire that is charged uniformly at $\lambda = 4.0 \times 10^{−6} \text{C}/\text{m} .$

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5.5 Exercise 13

Two thin parallel conducting plates are placed 2.0 cm apart. Each plate is 2.0 cm on a side; one plate carries a net charge of $8.0 \mu \text{C} ,$ and the other plate carries a net charge of $−8.0 \mu \text{C} .$ What is the charge density on the inside surface of each plate? What is the electric field between the plates?

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5.5 Exercise 17

Charge is distributed along the entire x-axis with uniform density $\lambda_{x}$ and along the entire y-axis with uniform density $\lambda_{y} .$ Calculate the resulting electric field at (a) $\overset{\rightarrow}{\text{r}} = a \hat{\text{i}} + b \hat{\text{j}}$ and (b) $\overset{\rightarrow}{\text{r}} = c \hat{\text{k}} .$

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5.5 Exercise 19

A proton moves in the electric field $\overset{\rightarrow}{\text{E}} = 200 \hat{\text{i}} \text{N}/\text{C} .$ (a) What are the force on and the acceleration of the proton? (b) Do the same calculation for an electron moving in this field.

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5.5 Exercise 21

A spherical water droplet of radius $25 \mu \text{m}$ carries an excess 250 electrons. What vertical electric field is needed to balance the gravitational force on the droplet at the surface of the earth?

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5.5 Exercise 27

A particle of mass m and charge $− q$ moves along a straight line away from a fixed particle of charge Q. When the distance between the two particles is $r_{0} , − q$ is moving with a speed $v_{0} .$ (a) Use the work-energy theorem to calculate the maximum separation of the charges. (b) What do you have to assume about $v_{0}$ to make this calculation? (c) What is the minimum value of $v_{0}$ such that $− q$ escapes from Q?

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