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16 Electrostatics
16-1 Electrostatic Force
Vocabulary Electrostatics: The study of electric charges, forces, and fields.
The symbol for electric charge is the letter “ q ” and the SI unit for charge is the coulomb (C). The coulumb is a very large unit.
1 C 6.25 1018 electrons or 1 electron has a charge of 1.60 10 ^19 C.
Electrons surrounding the nucleus of an atom carry a negative charge. Protons, found inside the nucleus of the atom, carry a positive charge of 1.60 10 ^19 C, while neutrons (which also reside in the nucleus) are neutral. It is important to remember that only electrons are free to move in a substance. Protons and neutrons usually do not move.
When two objects with like charges, positive or negative, are brought near each other, they experience a repulsive force. When objects with opposite charges, one negative and one positive, are brought side by side, they experience an attractive force. These forces can be described with Coulomb’s law.
Vocabulary Coulomb’s Law: Two charged objects attract each other with a force that is proportional to the charge on the objects and inversely proportional to the square of the distance between them.
F
This equation looks very similar to Newton’s law of universal gravitation. As before, the sign means “proportional to.” To make an equation out of this proportionality, insert a quantity called the electrostatic constant, k.
k 9.0 109 N m^2 /C 2
The magnitude of Coulomb’s law can now be written as an equation.
electrostatic force or F
kq 1 q 2 d^2
( electrostatic constant )( charge 1 )( charge 2 ) ( distance )^2
q 1 q 2 d^2
Like all other forces, the electrostatic force between two charged objects is measured in newtons.
Solved Examples
Example 1: Anthea rubs two latex balloons against her hair, causing the balloons to become charged negatively with 2.0 10 ^6 C. She holds them a distance of 0.70 m apart. a) What is the electric force between the two balloons? b) Is it one of attraction or repulsion?
Solution: a. It is not necessary to carry the sign of the charge throughout the entire exercise. However, when determining the direction of your final answer, it is important to remember the charge on each object.
Given: q 1 2.0 10 ^6 C Unknown: F ? q 2 2.0 10 ^6 C Original equation: F d 0.70 m k 9.0 109 N m^2 /C 2
Solve: F 0.073 N
b. Because both balloons are negatively charged, they will repel each other.
Example 2: Two pieces of puffed rice become equally charged as they are poured out of the box and into Kirk’s cereal bowl. If the force between the puffed rice pieces is 4 10 ^23 N when the pieces are 0.03 m apart, what is the charge on each of the pieces?
Solution: Because both charges are the same, solve for both q ’s together. Then find the square root of that value to determine one of the charges.
Given: F 4 10 ^23 N Unknown: q ? d 0.03 m Original equation: F k 9.0 109 N m^2 /C 2
Solve: q 1 q 2 4 10 ^36 C^2
This is the square of the charge on the pieces of puffed rice. To find the charge on one piece of puffed rice, take the square root of this number.
q (^24) 10 ^36 C^2 2 10 ^18 C
14 10 ^23 N2 10.03 m 22 9.0 10 9 N #^ m^2 >C^2
Fd^2 k
kq 1 q 2 d^2
1 9.0 10 9 N #^ m^2 >C^2 2 12.0 10 ^6 C2 12.0 10 ^6 C 2 1 0.70 m 22
kq 1 q 2 d^2
kq 1 q 2 d^2
d 2.7 10 ^3 m
2 kq 1 q 2 > F (^21) 9.0 109 N #^ m^2 >C^2 2 14.0 10 ^14 C 22 >12.0 10 ^12 N 2
d 10. m
2 kq 1 q 2 > F (^21) 9.0 109 N #^ m^2 >C^2 2 13.0 10 ^5 C 22 >18.1 10 ^2 N 2
2.7 10 ^3 m
10. m
Exercise 4: Bonnie is dusting the house and raises a cloud of dust particles as she wipes across a table. If two 4.0 10 ^14 -C pieces of dust exert an electrostatic force of 2.0 10 ^12 N on each other, how far apart are the dust particles at that time?
Answer:
Exercise 5: Each of two hot-air balloons acquires a charge of 3.0 10 ^5 C on its surface as it travels through the air. How far apart are the balloons if the electrostatic force between them is 8.1 10 ^2 N?
Answer:
