Q: An electric dipole with moment $$\mathbf{p} is $$placed in a uniform electric field $$\mathbf{E}. $$What is the torque experienced by the dipole?

$$\tau = \mathbf{p} \times \mathbf{E}$$

Q: A spherical water drop of diameter $$1.20\ \mu\text{m} is $$suspended in air by a downward electric field $$E = 462\ \text{N/C}. If $$the density of water is $$1.00 \times 10^3$\ \text{kg/m}^3$$, what is the weight of the drop?

$$8.87 \times 10$$^{-15}$$\ \text{N}$$

Q: An electron is released from rest in a uniform electric field of $$2.00 \times 10^4$\ \text{N/C}. $$What is the magnitude of its acceleration? (Electron mass $$m_e = 9.11 \times 10$$^{-31}$$\ \text{kg}$$, charge $$e = 1.602 \times 10$$^{-19}$$\ \text{C})$$

$$3.51 \times 10$$^{15}$$\ \text{m/s}^2$$

Q: A proton is accelerated from rest through a distance of $$1.00\ \text{cm} in a $$uniform electric field of $$2.00 \times 10^4$\ \text{N/C}. $$What is its final speed? (Proton mass $$m_p = 1.67 \times 10$$^{-27}$$\ \text{kg}$$, charge $$e = 1.60 \times 10$$^{-19}$$\ \text{C})$$

$$1.96 \times 10^5$\ \text{m/s}$$

Q: Two large parallel copper plates are $$5.0\ \text{cm}$$ apart. An electron is released from the negative plate and a proton from the positive plate at the same time. At what distance from the positive plate do they pass each other? ($$m_p = 1.67 \times 10$$^{-27}$$\ \text{kg}$$, $$m_e = 9.11 \times 10$$^{-31}$$\ \text{kg})$$

$$2.73 \times 10$$^{-5}$$\ \text{m}$$

Question 1

Which of the following best describes the direction of the electric field produced by a negative point charge?

Accepted Answer

The electric field points toward the negative charge.

Question 2

A small test charge $$q_0 is $$placed in an electric field $$\mathbf{E} at $$point $$\mathbf{r}. $$What is the force experienced by the test charge?

Accepted Answer

$$\mathbf{F} = q_0$ \mathbf{E}$$

Question 3

What is the SI unit of the electric field?

Accepted Answer

Newton per coulomb (N/C)

Question 4

A ring of charge with radius $$R$$ and total charge $$q$$ produces an electric field at a point on its axis a distance $$z$$ from the center. Which formula gives the magnitude of the electric field at that point?

Accepted Answer

$$E = \dfrac{qz}{4\pi\$$epsilon_0$$(z^2$$ + $$R^2$$)^{3/2}$$}$$

Question 5

A disk of radius $$R$$ has a uniform surface charge density $$\sigma. $$What is the electric field at a point on its axis a distance $$z$$ from the center?

Accepted Answer

$$E = \dfrac{\sigma}{2\$$epsilon_0$$}\left(1 - \dfrac{z}{\sqrt{z^2$ + R^2$}}\right)$$

Question 6

An electric dipole with moment $$\mathbf{p} is $$placed in a uniform electric field $$\mathbf{E}. $$What is the torque experienced by the dipole?

Accepted Answer

$$	au = \mathbf{p} 	imes \mathbf{E}$$

Question 7

A spherical water drop of diameter $$1.20\ \mu	ext{m} is $$suspended in air by a downward electric field $$E = 462\ 	ext{N/C}. If $$the density of water is $$1.00 	imes 10^3$\ 	ext{kg/m}^3$$, what is the weight of the drop?

Accepted Answer

$$8.87 	imes 10$$^{-15}$$\ 	ext{N}$$

Question 8

An electron is released from rest in a uniform electric field of $$2.00 	imes 10^4$\ 	ext{N/C}. $$What is the magnitude of its acceleration? (Electron mass $$m_e = 9.11 	imes 10$$^{-31}$$\ 	ext{kg}$$, charge $$e = 1.602 	imes 10$$^{-19}$$\ 	ext{C})$$

Accepted Answer

$$3.51 	imes 10$$^{15}$$\ 	ext{m/s}^2$$

Question 9

A point charge $$q is $$placed at the origin. What is the electric field at a distance $$r$$ from the charge?

Accepted Answer

$$\mathbf{E} = \dfrac{kq}{r^2$}\hat{r}$$

Question 10

A disk of radius $$2.5\ 	ext{cm}$$ has a surface charge density $$5.3\ \mu	ext{C/m}^2. $$What is the magnitude of the electric field produced by the disk at a point on its central axis at $$z = 12\ 	ext{cm}$$?

Accepted Answer

$$629\ 	ext{N/C}$$

Question 11

A proton is accelerated from rest through a distance of $$1.00\ 	ext{cm} in a $$uniform electric field of $$2.00 	imes 10^4$\ 	ext{N/C}. $$What is its final speed? (Proton mass $$m_p = 1.67 	imes 10$$^{-27}$$\ 	ext{kg}$$, charge $$e = 1.60 	imes 10$$^{-19}$$\ 	ext{C})$$

Accepted Answer

$$1.96 	imes 10^5$\ 	ext{m/s}$$

Question 12

Two large parallel copper plates are $$5.0\ 	ext{cm}$$ apart. An electron is released from the negative plate and a proton from the positive plate at the same time. At what distance from the positive plate do they pass each other? ($$m_p = 1.67 	imes 10$$^{-27}$$\ 	ext{kg}$$, $$m_e = 9.11 	imes 10$$^{-31}$$\ 	ext{kg})$$

Accepted Answer

$$2.73 	imes 10$$^{-5}$$\ 	ext{m}$$

Question 13

An electron in a particle beam has kinetic energy $$1.60 	imes 10$$^{-17}$$\ 	ext{J}. $$What is the magnitude of the electric field required to stop the electron in $$10.0\ 	ext{cm}$$?

Accepted Answer

$$1.00 	imes 10^3$\ 	ext{N/C}$$

Question 14

Which statement about electric field lines is correct?

Accepted Answer

The number of field lines originating from a charge should be proportional to the charge.

Question 15

An electron is constrained to the central axis of a ring of charge with radius $$R$$ and total charge $$q. $$For small oscillations, what is the angular frequency $$\omega of $$the electron's motion?

Accepted Answer

$$\omega = \sqrt{\dfrac{eq}{4\pi\$$epsilon_0$$ m R^3$}}$$

Question 16

A point charge $$q$$ creates an electric field of $$1.00\ 	ext{N/C} at $$points $$1.00\ 	ext{m}$$ away. What is the magnitude of the charge?

Accepted Answer

$$1.11 	imes 10$$^{-10}$$\ 	ext{C}$$

Question 17

A charged object with $$q = 24\ \mu	ext{C} is $$placed in a uniform electric field $$E = 610\ 	ext{N/C}$$ and floats. What is its mass? ($$g = 9.80\ 	ext{m/s}^2)$$

Accepted Answer

$$1.5 	imes 10$$^{-3}$$\ 	ext{kg}$$

Question 18

A dipole with moment $$\mathbf{p} is $$placed in a uniform electric field $$\mathbf{E}. $$What is its potential energy?

Accepted Answer

$$U = -\mathbf{p} \cdot \mathbf{E}$$

Question 19

A proton and an electron are placed at rest in an electric field of $$520\ 	ext{N/C}. $$What is the speed of the electron after $$48\ 	ext{ns}$$?

Accepted Answer

$$4.4 	imes 10^6$\ 	ext{m/s}$$

Electric Fields: Concepts, Calculations, and Applications

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