﻿ ﻿STATIC ELECTRICITY - PHYSICS TOPIC REVIEW - SAT Subject Test Physics

## SAT Subject Test Physics (2012)

### Chapter 12. STATIC ELECTRICITY

A bright flash of lightning and the shock you receive when touching a doorknob have something in common. They both involve electric charges. In this chapter, you will review the buildup of electric charges, or static electricity. In the next chapter, you will review the flow of electric charges as current through circuits.

Electric Charge

Matter is made up of atoms, which in turn are made up of particles. One of those particles, the electron (e), carries a negative electric charge. The symbol for charge is q, and the SI unit of charge is the Coulomb (C). The charge of an electron is –1.6 × 10–19 C. A proton carries a charge that is equal in magnitude to that of an electron, but has a positive value of 1.6 × 10–19 C. In addition to electrons and protons, neutrons are also found within atoms. Neutrons are electrically neutral.

Objects become charged when electrons are transferred from one to another. Objects described as negatively charged have a surplus of electrons, whereas objects described as positively charged have a deficiency of electrons. Charges are conserved whenever they are transferred, which means that electric charges are neither created nor destroyed. For example, when a rubber rod is stroked with a piece of wool, electrons are transferred from the wool to the rubber. As a result, the rubber rod becomes negatively charged because it gains electrons and the wool becomes positively charged because it loses electrons.

Conversely, if a glass rod is rubbed with a piece of silk, electrons are transferred from the glass to the silk. In this case, the glass rod becomes positively charged because it loses electrons, and the silk becomes negatively charged because it gains electrons. In each case, the net loss of electrons by one object equals the net gain of electrons by the other object. Charge is conserved.

The law of charges states that unlike charges attract one another, and like charges repel one another. The same is true for charged objects such as the rods and cloths described earlier. The law of charges is easily demonstrated with the use of pith balls suspended from strings thin enough to be considered massless. Two positively charged pith balls or two negatively charged pith balls will repel one another. A positively charged pith ball and a negatively charged pith ball will attract one another.

Coulomb’s Law

The attraction or repulsion between charged particles constitutes an electric force. The magnitude of the force between charged particles FE is proportional to the product of the two charges (q1 and q2) and varies inversely as the square of the distance between them (r2). This relationship is known as Coulomb’s Law.

The k represents the proportionality constant, which is equal to 9 × 109 N · m2/C2. SAT Physics will most likely ask about your understanding of the relationships described by Coulomb’s Law rather than specific recall of the equation and calculations using it. If calculations are required, you will be provided with the value of k.

Example:

Two point charges q1 and q2 are separated by distance r. What happens to the electric force between these two charges if the distance is halved?

Substitute ½r into the equation for Coulomb’s Law.

Electroscope

An electroscope is an instrument used to determine the presence of small electric charges. It consists of two thin metal leaves suspended from a metal knob. The metal leaves hang down when not charged. When a negatively charged object is brought near the metal knob at the top, the electrons in the knob are repelled into the leaves. The knob becomes positively charged and both leaves become negatively charged. Because the same charge is transferred to each leaf, they repel one another and separate.

If, instead, a positively charge object is brought near the metal knob at the top, electrons are drawn into knob. The knob becomes negatively charged, and the leaves become positively charged. Again, the leaves have the same charge, so they repel one another and separate.

Electric Field

An electric field exists in the space around an electric charge where another charge will experience a force. An electric field can be visualized by drawing arrows known as electric field lines. Each line points in the direction in which a positive test charge would experience a force. A positive test charge would be repelled by a positive charge, so the electric field lines point outward from a positive charge. A positive test charge would be attracted toward a negative charge, so the electric field lines point inward toward a negative charge.

When two charges are brought near one another, the lines become curved as shown in the following diagram. The lines curve away from like charges and toward unlike charges.

The magnitude of the electric field is known as the electric field intensity E. Another way to describe this quantity is as the force per unit charge in a region of space. The relationship is described by the following equation.

The SI units of electric field intensity are newtons per Coulomb (N/C).

According to Coulomb’s Law, the electric force between two point charges is given by . Therefore, you can rewrite electric field intensity as shown here.

Viewing the equation in this format shows that the electric field at a given point depends on the charge of the object establishing the field and the distance to a point in space.

Electric Potential

Moving a charge against an electric field requires work. The work required to move charge q between two points in an electric field is known as potential difference V.

The SI unit of work is the joule, and the unit of charge is the Coulomb, which makes the unit of electric potential the joule per coulomb, or volt.

Potential difference is essentially the same as electric potential. For electric potential, however, the work is defined as the amount required to bring a positive charge from infinity to some point. You will read more about electric potential in your review of electric circuits.

Test-Taking Hint

When answering questions, make sure you read through all the answer choices before deciding. Two answer choices may be very similar, so you could overlook the difference if you rush to choose one.

REVIEW QUESTIONS

Select the choice that best answers the question or completes the statement.

1. How does the charge of an electron compare to the charge of a proton?

(A) the charge of a proton is double the magnitude of the charge of an electron.

(B) the charge of a proton is the same as the charge of an electron.

(C) the charge of a proton is equal and opposite to the charge of an electron.

(D) the charge of a proton is half the magnitude of the charge of an electron.

(E) the charge of a proton is four times charge of an electron.

2. Two point charges q1 and q2 are separated by distance r. What happens to the electric force if the charges are doubled?

(A) it is quartered.

(B) it is halved.

(C) it remains the same.

(D) it is doubled.

3. Particle A with charge q exerts a force F to the right on a particle B with a charge of –2q. What is the magnitude and direction of the force exerted by particle B on particle A?

(A) F to the right

(B) F to the left

(C) ½ F to the right

(D) ½ F to the left

(E) 2F to the right

4. The electric force between two charges is negative. Which of the following statements must be true?

(A) Both charges must be positive.

(B) Both charges must be negative.

(C) One charge must be twice the magnitude of the other.

(D) The force must be directed toward the larger charge.

(E) The force between the particles must be attractive.

5. The diagram below represents the electric field between two point charges.

What must be true about the charges?

(A) A is positive and B is negative.

(B) A is positive and B is positive.

(C) A is negative and B is negative.

(D) A is negative and B is positive.

(E) A is neutral and B is neutral.

6. A rod is brought near the knob of an electroscope. The metal leaves separate. What can you conclude about the rod?

(A) It was electrically charged.

(B) It was electrically neutral.

(C) It was electrically negative.

(D) It was electrically positive.

(E) It was a source of electrons.

7. Charge q establishes an electric field. At a distance of 40 cm away, the strength is 60 N/C. What is the magnitude of the electric field strength at a distance of 80 cm away?

(A) 6 N/C

(B) 15 N/C

(C) 20 N/C

(D) 30 N/C

(E) 60 N/C

8. Which of the following is measured by electrical potential?

(A) force per unit charge

(B) distance between charges

(C) work per unit charge

(D) force between charges

(E) electric proportionality constant

Questions 9 and 10 relate to the diagram below, which shows two charges located along the x-axis.

9. What is the magnitude of the force F between the charges in terms of q1 and q2?

10. Suppose and . Where along the x-axis must a negative charge q3 be placed such that the resulting force on it is zero?

(A) 1.00 m

(B) 1.15 m

(C) 1.60 m

(D) 2.15 m

(E) 3.45 m

1. C Electrons and protons are charged particles within atoms. Despite the difference in mass, the magnitude of the charge on the particles is the same. However, the charge of an electron is considered negative, whereas the charge on a proton is positive.

2. E Substitute 2q1 and 2q2 into the equation for Coulomb’s Law.

3. B According to Coulomb’s Law, the forces exerted by each particle on the other are the same. Because the particles have opposite charges, an attractive force is established between them. Therefore, the magnitudes of the forces are the same, but the direction is opposite.

4. E According to Coulomb’s Law, like charges will result in a positive force so the charges must be unlike for the force to be negative. If the charges are unlike, the force between them will be attractive.

5. A Electric field lines represent the direction in which a positive test charge will experience a force. Because like charges repel one another, the test charge would be forced away from a positive charge and toward a negative charge. Thus, A must be positive and B must be negative.

6. A Like charges repel one another. For the leaves to separate, they had to be charged with like charges. The charges could be either positive or negative. The nature of each charge cannot be identified from the fact that the leaves of the electroscope separate.

7. B The electric field strength is inversely related to the square of the distance. Therefore, if the distance is doubled, the original value E is divided by 4.

8. C Electric potential is defined as the amount of work required to bring a positive charge from infinity to some point.

9.

10. C The force exerted on q3by q1 must equal the force exerted on q3by q2 for the forces to cancel.

The constant k and q3 drop out of the equation, making it . Substitute in the given values to get

which becomes

Rearrange to solve for , so , . Then. , so and .

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