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Learning Introductory Physics with Activities

Paul J. Emigh, Rebecka Tumblin, Kathryn Hadley, Danielle Skinner

Section 20.10 Practice - Electric Fields

Subsection A*R*C*S Practice

A*R*C*S 20.10.1. A Piece of Pollen.

A piece of pollen typically has both a small mass (about \(5 \mathrm{~ng}\)) and a small amount of charge (about \(1 \mathrm{~fC}\)). Estimate the electric field that a honeybee needs to create to carry a typical piece of pollen.

A*R*C*S 20.10.2. Electric Field Components.

The electric field at a point in space due to a nearby collection of charges is \(\vec{E} = 400 \hat{x} + 100 \hat{y}\) \(N/C \text{.}\)
  1. What is the electric force on a proton if placed at this point? Give your answer in component form.
  2. What is the electric force on an electron if placed at this point? Give your answer in component form.
  3. What is the magnitude of the acceleration of a proton if placed at this point?
  4. What is the magnitude of the acceleration of an electron if placed at this point?

A*R*C*S 20.10.3. A Hydrogen Atom.

In a simple model of the hydrogen atom, the electron moves in a circular orbit of a radius \(0.053\) \(nm\) around a stationary proton. How many revolutions per second does the electron make?

A*R*C*S 20.10.4. Charged Pendulum.

Two \(5.0\) \(g\) point charges on \(1.0\) \(m\) long threads are charged to \(+100.0\) \(nC\text{.}\) Determine the unknown angle \(\theta\text{.}\) You can assume that \(\theta\) is a small angle.
Figure 20.10.1. A charged pendulum.

A*R*C*S 20.10.5. Charge on a Spring.

An ideal spring has spring constant \(k_s\) (to distinguish it from the electrostatic constant \(k\)) and equilibrium length \(l\text{.}\) Then, you glue two identical negative point charges to the ends of the spring and observe that the equilibrium length doubles. Determine the amount of charge on each end of the spring.

Subsection Numerical Practice

Calculation 20.10.6. Net Charge I.

In a laboratory, a system is constructed that contains 7 protons and 4 electrons.  What is the net charge of this system?
Answer.
\(4.8 \times 10^{-19} \mathrm{~C}\)

Calculation 20.10.7. Net Charge II.

A system of protons and electrons has a net charge of \(-1.12 \times 10^{-18} \mathrm{~C}\text{.}\) If the system contains 15 protons, how many electrons are in the system?
Answer.
\(22\) electrons

Calculation 20.10.8. Net Charge III.

An amoeba has \(1 \times 10^{16}\) protons and a net charge of \(0.300 \mathrm{~pC}\text{.}\) How many fewer electrons are there than protons?
Answer.
\(1.88 \times 10^6\) fewer electrons

Calculation 20.10.9. Dryer Charge.

Consider a cotton sock inside a dryer machine whose drum (inner container) is made of steel. After tumbling around in the dryer’s drum for a while, the cotton sock has a net charge on it now. Which of the following charge transfers most likely happened in this sock-drum system?
  1. The steel drum lost electrons while the cotton sock gained those electrons.
  2. The steel drum lost protons while the cotton sock gained those protons.
  3. The cotton sock lost electrons while the steel drum gained those electrons.
  4. The cotton sock lost protons while the steel drum gained those protons.
  5. Both the cotton sock and steel drum lost electrons.
  6. Both the cotton sock and the steel drum gained electrons.
Answer.
C

Calculation 20.10.10. Electric Field of a Point Charge.

Consider a positive charge \(q_1\) = 4 .00 nC that exists in a space far away from other charges. What is the electric field at a point P in space that is 15.0 m to the left of this point charge?
Answer.
\(\vec{E} = (-0.16 \mathrm{N}/\mathrm{C}) \hat{x}\)

Calculation 20.10.11. Charge on a Penny.

A 2.5-g copper penny is given a charge of \(-2.0 \times 10^{-9} \ \mathrm{C}\text{.}\)
  1. How many excess electrons are on the penny?
  2. By what percent do the excess electrons change the mass of the penny?
Answer 1.
\(1.137 \times 10^{10}\) electrons
Answer 2.
\(4.545 \times 10^{-16} \%\)

Calculation 20.10.12. Proton and Electron.

An electron and a proton are \(3.00 \mathrm{~\mu m}\) apart from each other. What is the magnitude of the electric force by the proton on the electron?
Answer.
\(2.56 \times 10^{-17} \mathrm{~N}\)

Calculation 20.10.13. Charged Spheres.

Problem Statement: Consider two small, charged spheres, \(q_1\) and \(q_2\text{,}\) a distance \(\Delta x\) apart.
  1. If \(\Delta x\) increases by a factor of \(16/9\text{,}\) and \(q_1\) and \(q_2\) remain the same, by what factor does the force between the two change?
  2. If \(\Delta x\) increases by a factor of \(4/\sqrt{2}\text{,}\) \(q_1\) increases by a factor of \(2\text{,}\) and \(q_2\) increases by a factor of \(\sqrt{2}\text{,}\) by what factor does the force between the two change?
Answer.
  1. \(\displaystyle 81/256\)
  2. \(\displaystyle \sqrt{2}/4\)

Calculation 20.10.14. Charge in an Electric Field.

A -3.00 C charge is placed in an external electric field. It is observed that the electric force on this charge is \(\vec{F} = (9 \mathrm{N}) \hat{x} + (3 \mathrm{N}) \hat{y} + (-6 \mathrm{N}) \hat{z}\text{.}\) What is the external electric field?
Answer.
\(\vec{E} = (-3 \mathrm{N/C}) \hat{x} + (-1 \mathrm{N/C}) \hat{y} + (2 \mathrm{N/C}) \hat{z}\)

Calculation 20.10.15. Electron in an Electric Field I.

An electron is traveling in the negative x-direction when an external electric field pointing in the positive x-direction is turned on in that region. Which of the following statements are true about the electron right after the field is turned on?
  1. It experiences a force in the positive x-direction.
  2. It experiences a force in the negative x-direction.
  3. It travels in the positive x-direction.
  4. It travels in the negative x-direction.
  5. It accelerates in the positive x-direction.
  6. It accelerates in the negative x-direction.
  7. It begins to slow down.
  8. It starts to speed up.
Answer.
(2), (4), (6), (8)

Calculation 20.10.16. Electron in an Electric Field II.

An electron is traveling with a velocity that has equal positive x and y components.  Suddenly an electric field is turned on in the positive y-direction in this region.  Which of the following statements are true about the electron right after the field is turned on?
  1. It accelerates in the positive x-direction.
  2. It accelerates in the negative x-direction.
  3. It accelerates in the positive y-direction.
  4. It accelerates in the negative y-direction.
  5. It begins to slow down.
  6. It starts to speed up.
Answer.
(4), (5)

Calculation 20.10.17. Charged Object on Earth.

A 4.00 kg object with a net charge of -2.00 C is placed at rest above the surface of the Earth.  There also exists a uniform external electric field of magnitude 3.00 N/C pointing directly downward.  When released, what is the magnitude of the acceleration of this object?
Answer.
\(8.30 \ \mathrm{m}/\mathrm{s}^2\)

Calculation 20.10.18. Charged Balls on Strings.

Figure 20.10.2. Two charged balls attached to strings.
Two small balls, each of mass 5.0 g, are attached to silk threads 50 cm long, which are in turn tied to the same point on the ceiling, as shown above. When the balls are given the same charge Q, the threads hang at \(5.0^\circ\) to the vertical. What is the magnitude of Q? What are the signs of the two charges?
Answer.
\(Q = 6.1 \times 10^{-8} \ \mathrm{C}\text{.}\) The charges can be positive or negative, but both have to be the same sign.

References References

[1]
Practice activities provided by BoxSand: https://boxsand.physics.oregonstate.edu/welcome.
[2]
Practice activities provided by Ling, S. J., Moebs, W., & Sanny, J. (2016). Electric Charges and Fields. In University Physics Volume 2. OpenStax.
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