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# Chapter 13: Basic Physics SE-Electrostatics

Difficulty Level: At Grade Created by: CK-12

The Big Idea

Conservation of charge is the fourth of the 5 conservation laws in physics. There are two charges, + and -, and the symmetry of the electric charge indicates that the total charge in the universe remains the same. In any closed system, charge can be transferred from one body to another but the amount of electric charge in the universe remains the same.

Electromagnetism is associated with charge and is a fundamental force of nature like gravity. If charges are static (i.e. not moving) the electromagnetic force is the Coulomb electric force. In the same way that the gravitational force depends on mass, the Coulomb electric force depends on the property known as electric charge. Like gravity the Coulomb electric Force decreases with the square of the distance. The Coulomb electric force is responsible for many of the forces discussed previously: the normal force, contact forces, friction, and so on… all of these forces arise in the mutual attraction and repulsion of charged particles.

The law determining the magnitude of the Coulomb electric force has the same form as the law of gravity. The electric constant is 20 orders of magnitude greater than the gravitational constant. That is why electricity normally dominates gravity at the atomic and molecular level. However, gravity will dominate in large bodies. The reason is that atoms and molecules have equal number of positive and negative charges and are therefore electrically neutral (thus the Coulomb electric force is canceled out).

Key Equations

• \begin{align*}q = Ne\end{align*} ; the total charge of an object is always some integer \begin{align*}N\end{align*} multiplied by the fundamental charge \begin{align*}e = 1.6 \times 10^{-19}\ C\end{align*}.
• \begin{align*}F = \frac{kq_1q_2}{r^2}\end{align*} ; the force exerted by two charges on one another depends on the amount of the charge, the distance between them, and a fundamental constant \begin{align*}k = 9 \times 10^9 Nm^2/C^2\end{align*}.
• \begin{align*}F = qE\end{align*} ; a charged object in an electric field feels a force.
• \begin{align*}E = \frac{kq}{r^2}\end{align*} ; the electric field produced by a charged object depends on the charge of the object and the distance to the object. through a changing electric potential.
• \begin{align*}E = \frac{- \Delta V}{\Delta x}\end{align*} ; the electric field depends on how quickly the electric potential varies over space; alternatively \begin{align*}\Delta V = - E \cdot \Delta x\end{align*}.
• \begin{align*}V = \frac{kq}{r}\end{align*} ; the electric potential produced by a charged object depends on the charge of the object and the distance to the object.

Key Concepts

• In any process, electric charge is conserved. The total electric charge of the universe does not change. Therefore, electric charge can only be transferred – not lost – from one body to another.
• Electrons have negative charge and protons have positive charge. The magnitude of the charge is the same for both, \begin{align*}e = 1.6 \times 10^{-19}\ C\end{align*}.
• Normally, electric charge is transferred when electrons leave the outer orbits of the atoms of one body (leaving it positively charged) and move to the surface of another body (causing the new surface to gain a negative net charge). In a plasma all electrons are stripped from the atoms, leaving positively charged ions and free electrons.
• Similarly charged objects have a repulsive force between them. Oppositely charged objects have an attractive force between them.
• The value of the electric field tells you the force that a charged object would feel if it entered this field. Electric field lines tell you the direction a positive charge would go if it were placed in the field.
• Electric potential is measured in units of Volts \begin{align*}(V)\end{align*} – thus electric potential is often referred to as “voltage.”
• Positive charges move towards lower electric potential; negative charges move toward higher electric potential

Key Applications

• In problems that ask for excess negative or positive charge, remember that each electron has one unit of the fundamental charge \begin{align*}e\end{align*}.
• To find the speed of a particle after it traverses a voltage difference, use the equation for the conservation of energy: \begin{align*}q \Delta V = \frac{1}{2}mv^2\end{align*}
• Force and electric field are vectors and thus have direction as well as their value.
• Electric field lines point from high electric potential to low potential and are perpendicular to the electric potential line. Note that this agrees with the fact that electric field lines tell you the direction a positive charge would travel, since positive charges go from high potential (i.e. big voltage) to low potential (i.e. low voltage).

Electricity Problem Set

1. After sliding your feet across the rug, you touch the sink faucet and get shocked. Explain what is happening.
2. What is the net charge of the universe? Of your toaster?
3. As you slide your feet along the carpet, you pick up a net charge of +4 mC. Which of the following is true?
1. You have an excess of \begin{align*}2.5 \times 10^{16}\end{align*} electrons
2. You have an excess of \begin{align*}2.5 \times 10^{19}\end{align*} electrons
3. You have an excess of \begin{align*}2.5 \times 10^{16}\end{align*} protons
4. You have an excess of \begin{align*}2.5 \times 10^{19}\end{align*} protons
4. You rub a glass rod with a piece of fur. If the rod now has a charge of \begin{align*} -0.6 \ \mu C\end{align*}, how many electrons have been added to the rod?
1. \begin{align*}3.75 \times 10^{18}\end{align*}
2. \begin{align*}3.75 \times 10^{12}\end{align*}
3. 6000
4. \begin{align*}6.00 \times 10^{12}\end{align*}
5. Not enough information
5. What is the direction of the electric field if an electron initially at rest begins to move in the North direction as a result of the field?
1. North
2. East
3. West
4. South
5. Not enough information
6. Two metal plates have gained excess electrons in differing amounts through the application of rabbit fur. The arrows indicate the direction of the electric field which has resulted. Three electric potential lines, labeled \begin{align*}A, B,\end{align*} and \begin{align*}C\end{align*} are shown. Order them from the greatest electric potential to the least.
1. \begin{align*}A, B, C\end{align*}
2. \begin{align*}C, B, A\end{align*}
3. \begin{align*}B, A, C\end{align*}
4. \begin{align*}B, C, A\end{align*}
5. \begin{align*}A = B = C\end{align*}... they’re all at the same potential
7. The diagram to the right shows a negatively charged electron. Order the electric potential lines from greatest to least.
1. \begin{align*}A, B, C\end{align*}
2. \begin{align*}C, B, A\end{align*}
3. \begin{align*}B, A, C\end{align*}
4. \begin{align*}B, C, A\end{align*}
5. \begin{align*}A = B = C\end{align*} ... they’re all at the same electric potential
8. The three arrows shown here represent the magnitudes of the electric field and the directions at the tail end of each arrow. Consider the distribution of charges which would lead to this arrangement of electric fields. Which of the following is most likely to be the case here?
1. A positive charge is located at point \begin{align*}A\end{align*}
2. A negative charge is located at point \begin{align*}B\end{align*}
3. A positive charge is located at point \begin{align*}B\end{align*} and a negative charge is located at point \begin{align*}C\end{align*}
4. A positive charge is located at point \begin{align*}A\end{align*} and a negative charge is located at point \begin{align*}C\end{align*}
5. Both answers a) and b) are possible
9. Particles \begin{align*}A\end{align*} and \begin{align*}B\end{align*} are both positively charged. The arrows shown indicate the direction of the forces acting on them due to an applied electric field (not shown in the picture). For each, draw in the electric field lines that would best match the observed force.
10. To the right are the electric potential lines for a certain arrangement of charges. Draw the direction of the electric field for all the black dots.
11. A suspended pith ball possessing \begin{align*}+10 \ \mu C\end{align*} of charge is placed 0.02 m away from a metal plate possessing \begin{align*}-6 \ \mu C\end{align*} of charge.
1. Are these objects attracted or repulsed?
2. What is the force on the negatively charged object?
3. What is the force on the positively charged object?
12. Consider the hydrogen atom. Does the electron orbit the proton due to the force of gravity or the electric force? Calculate both forces and compare them. (You may need to look up what is inside the hydrogen atom to complete this problem.)
13. As a great magic trick, you will float your little sister in the air using the force of opposing electric charges. If your sister has 40 kg of mass and you wish to float her 0.5 m in the air, how much charge do you need to deposit both on her and on a metal plate directly below her? Assume an equal amount of charge on both the plate and your sister.
14. Copy the arrangement of charges below. Draw the electric field from the –2 C charge in one color and the electric field from the +2 C charge in a different color. Be sure to indicate the directions with arrows. Now take the individual electric field vectors, add them together, and draw the resultant vector. This is the electric field created by the two charges together.
15. Miriam wants to recharge her dead 12-V car. If she sends 28,000 C of charge into the terminals,
1. how much electrical potential energy will the battery store?
2. If all this electrical PE was converted into heat energy, what mass of water at \begin{align*}100^\circ C\end{align*} could be boiled away into steam?
16. Let’s say a Van de Graff generator has \begin{align*}1 \times 10^6\end{align*} electrons on its dome, via the rubber belt inside. The dome of the generator is at a potential of 10 million volts.
1. How much energy is transferred when the charge jumps to ground?
2. If you had an equivalent amount of energy in the form of the kinetic energy of a moving 100-g bullet, how fast would the bullet be moving?
17. Sitting on his porch one sultry summer evening, Boris sips a mint julep and listens to the sound of the “bug zapper” killing mosquitoes. If two plates in a bug zapper are 6.0 cm apart and create an electric field of \begin{align*}3 \times 10^6 \ V/m\end{align*} between them, what is the potential difference across the plates?
18. A lightning bolt hits the Menlo swimming pool after passing through a potential difference of \begin{align*}10^8 \ V\end{align*}. If the lightning bolt vaporizes 1000 kg of water in that was originally at a temperature of \begin{align*}20.0 ^\circ C\end{align*},
1. How much energy did it transfer? (HINT: calculate the amount of heat required to raise temp of water and boil it)
2. If one assumes all of the lightning bolt energy was deposited in the water, how much charge was the lightning bolt carrying to supply that much energy across a potential of \begin{align*}10^8 \ V\end{align*}?
19. Collisions of electrons with the surface of your television set give rise to the images you see. How are the electrons accelerated to high speed? Consider the following: two metal plates (The right hand one has small holes allow electrons to pass through to the surface of the screen.), separated by 30 cm, have a uniform electric field between them of 400 N/C. Note that the arrows in the picture show the direction the electrons are going, the electric field is going the other way.
1. Find the force on an electron located at a point midway between the plates
2. Find the voltage difference between the two plates
3. Find the speed of the electron just before striking the front plate (the screen of your TV)
4. Suppose your TV tube had a proton instead (it doesn’t - just pretend). Considering that the charge on a proton is equal and opposite to that on an electron, and the mass of the proton is \begin{align*}1.67 \times 10-27 \ kg\end{align*}, how would your answers to a-c be different? Would the proton accelerate in the same direction as the electron? Would it still gain KE?
20. A proton traveling to the right moves in-between the two large plates. A vertical electric field, pointing upwards with magnitude 3.0 N/C, is produced by the plates.
1. What is the direction of the force on the proton when between the plates?
2. Draw the electric field lines on the diagram.
3. If the electric field is 3.0 N/C, what is the acceleration and direction of the proton in the region of the plates?
4. Ignore the force of gravity (it is too small compared to electro force to be a factor) and sketch the path of the proton as it travels through the plates.

1. (b) 1350 N (c) 1350 N
2. \begin{align*}F_G = 1.0 \times 10^{-47}\ N\end{align*} and \begin{align*}F_e = 2.3 \times 10^{-8}\ N\end{align*}. The electric force is 39 orders of magnitudes bigger.
3. \begin{align*}1.0 \times 10^{-4}\ C\end{align*}
1. \begin{align*}3.36 \times 10^5 \ J\end{align*}
1. \begin{align*}1.6 \times 10^{-6}\ J\end{align*}
2. 0.0057 m/s
1. \begin{align*}1.8 \times 10^5 \ V\end{align*}
1. \begin{align*}620 \times 10^6 \ cal\end{align*}
2. 26 C
1. \begin{align*}6.4 \times 10^{-17}\ N\end{align*}
2. 120V
3. \begin{align*}6.5 \times 10^6 \ m/s\end{align*}
1. down
2. Up
3. \begin{align*}4.8 \times 10^{-19}\ N\end{align*}
4. \begin{align*}2.9 \times 10^8 \ m/s^2\end{align*}

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