Q: Eight point charges, each with charge $$q = 100\ \text{nC}$$, are placed at the corners of a cube with side length $$10\ \text{cm}. If $$the electric potential is defined to be zero at infinity, what is the electric potential at the center of the cube?

$$8.0 \times 10^3$\ \text{Volts}$$

Q: A line segment with charge density $$\lambda = 34\ \text{nC/m}$$ extends along the positive x-axis from $$x = 0 to$$ $$x = 50\ \text{cm}. At $$which of the following points does the electric field point parallel to the z-axis?

$$(x, y, z) = (25\ \text{cm}, 0, 25\ \text{cm})$$

Q: Three point charges, each equal to $$72\ \text{nC}$$, are arranged in an equilateral triangle with side length $$1\ \text{m}. $$What is the magnitude of the electrostatic force on one of the charges from the combined electric field of the other two?

$$2.8 \times 10$$^{-3}$$\ \text{N}$$

Q: A parallel-plate capacitor has plates with charge density $$5.5\ \text{nC/cm}^2. $$The separation between the plates is $$1\ \text{mm}. If $$the potential difference between the plates is $$5.1\ \text{V}$$, what is the magnitude of the electric field between the plates?

$$5.1 \times 10^3$\ \text{V/m}$$

Q: Suppose there is a semi-infinite line charge along the positive $$x-$$axis with charge density $$287\ \text{nC/m}. $$What is the magnitude of the $$y-$$component of the electric field at the position $$(x, y) = (0, 2\ \text{cm})$$?

$$2.6 \times 10^7$\ \text{N/C}$$

Q: An ideal electric dipole with magnitude $$1.25 \times 10$$^{-17}$$\ \text{C}\cdot\text{m} is $$placed in a region where the electric field points along the $$z-$$axis. If the field is being switched with the plates aligned with the dipole, what is the energy change?

$$2.94 \times 10$$^{-17}$$\ \text{Joules}$$

Question 1

Eight point charges, each with charge $$q = 100\ 	ext{nC}$$, are placed at the corners of a cube with side length $$10\ 	ext{cm}. If $$the electric potential is defined to be zero at infinity, what is the electric potential at the center of the cube?

Accepted Answer

$$8.0 	imes 10^3$\ 	ext{Volts}$$

Question 2

A line segment with charge density $$\lambda = 34\ 	ext{nC/m}$$ extends along the positive x-axis from $$x = 0 to$$ $$x = 50\ 	ext{cm}. At $$which of the following points does the electric field point parallel to the z-axis?

Accepted Answer

$$(x, y, z) = (25\ 	ext{cm}, 0, 25\ 	ext{cm})$$

Question 3

Four point charges, each with charge $$q = 7.0\ 	ext{nC}$$, are arranged in a square with side length $$20\ 	ext{cm}. $$What is the electric potential at the center of one of the sides of the square?

Accepted Answer

$$21\ 	ext{Volts}$$

Question 4

A ring of charge with radius $$5\ 	ext{cm} is $$centered at the origin and located in the $$xy-$$plane. The ring has total charge of $$4\ \mu	ext{C}. An $$ideal dipole with dipole moment $$10^{-12}$$\ 	ext{C}\cdot	ext{m}$$ is located along the positive z$-axis at z = 5$$\ 	ext{cm}$$. What is the preferred orientation of the dipole?

Accepted Answer

Parallel to the $$z-$$axis

Question 5

A point charge of $$5\ \mu	ext{C} is at $$the origin. A point charge of $$-1\ \mu	ext{C} is $$located at $$x = 5\ 	ext{m}. $$Assuming the electric potential is defined to be zero at infinity, at what other point(s) on the $$x-$$axis (in meters) is the electric potential zero?

Accepted Answer

$$x = 4$$ and $$x = 7$$

Question 6

Four point charges, each with charge $$q = 50\ 	ext{nC}$$, are arranged in a square with side length $$10\ 	ext{cm}. If a $$proton is at the center of the square and given an initial velocity of $$10^7$$\ 	ext{m/s}$$ in the +x$ direction, what is the maximum distance the proton can travel away from the square before its velocity becomes zero? (Assume the mass of a proton is 1.67$$ 	imes $$10^{-27}$$\ 	ext{kg}$$ and the charge of a proton is 1.60$$ 	imes $$10^{-19}$$\ 	ext{C}$$.)

Accepted Answer

$$0.18\ 	ext{m}$$

Question 7

Three point charges, each equal to $$72\ 	ext{nC}$$, are arranged in an equilateral triangle with side length $$1\ 	ext{m}. $$What is the magnitude of the electrostatic force on one of the charges from the combined electric field of the other two?

Accepted Answer

$$2.8 	imes 10$$^{-3}$$\ 	ext{N}$$

Question 8

A parallel-plate capacitor has plates with charge density $$5.5\ 	ext{nC/cm}^2. $$The separation between the plates is $$1\ 	ext{mm}. If $$the potential difference between the plates is $$5.1\ 	ext{V}$$, what is the magnitude of the electric field between the plates?

Accepted Answer

$$5.1 	imes 10^3$\ 	ext{V/m}$$

Question 9

Which of the following is true about a conducting object in electrostatic equilibrium?

Accepted Answer

The electric field within the body of the conductor must be zero

Question 10

Suppose there is a semi-infinite line charge along the positive $$x-$$axis with charge density $$287\ 	ext{nC/m}. $$What is the magnitude of the $$y-$$component of the electric field at the position $$(x, y) = (0, 2\ 	ext{cm})$$?

Accepted Answer

$$2.6 	imes 10^7$\ 	ext{N/C}$$

Question 11

A parallel-plate capacitor is charged so that the plates have equal and opposite charge densities $$\sigma = 5\ \mu	ext{C/m}^2. $$What is the electric field between the plates?

Accepted Answer

$$E = \frac{\sigma}{\$$varepsilon_0$$}$$

Question 12

An ideal electric dipole with magnitude $$1.25 	imes 10$$^{-17}$$\ 	ext{C}\cdot	ext{m} is $$placed in a region where the electric field points along the $$z-$$axis. If the field is being switched with the plates aligned with the dipole, what is the energy change?

Accepted Answer

$$2.94 	imes 10$$^{-17}$$\ 	ext{Joules}$$

Question 13

A neutral conducting sphere $$S is $$brought near a positively charged conductor, but not so near that they touch. What happens to the charge distribution on the surface of sphere $$S$$?

Accepted Answer

Negative charges accumulate on the side nearest the conductor

Question 14

Two parallel infinite planes of charge are located at $$z = 0$$ and $$z = 1\ 	ext{m}$$, with charge densities $$5\ \mu	ext{C/m}^2$$ and $$-3\ \mu	ext{C/m}^2$$ respectively. What is the electric field in the region $$z \u003e 1\ 	ext{m}$$?

Accepted Answer

$$E = \frac{\$$sigma_1$$ + \$$sigma_2$$}{\$$varepsilon_0$$}$$

Question 15

A ring of charge with radius $$5\ 	ext{cm} is $$centered at the origin and located in the $$xy-$$plane. The ring has total charge of $$4\ \mu	ext{C}. An $$ideal dipole with dipole moment $$10^{-12}$$\ 	ext{C}\cdot	ext{m}$$ is located along the positive z$-axis at z = 5$$\ 	ext{cm}$$. What is the preferred orientation of the dipole?

Accepted Answer

Parallel to the $$z-$$axis

Question 16

A conducting sphere is brought into contact with a positively charged conductor and then removed. What is the charge distribution on the sphere after this interaction?

Accepted Answer

The sphere acquires a uniform positive charge

Question 17

A semi-infinite line charge along the positive $$x-$$axis has charge density $$\lambda = 87\ 	ext{nC/m}. $$What is the $$y-$$component of the electric field at $$(x, y) = (0, 5\ 	ext{cm})$$?

Accepted Answer

$$1.09 	imes 10^7$\ 	ext{N/C}$$

Physics 2321 Midterm I: Electrostatics and Electric Fields Study Guide

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