Physics the Law of Electrostatic Force Key

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  1019 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  1019 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 q1q2 d2 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  m2/C2 The magnitude of Coulomb’s law can now be written as an equation. electrostatic force  (electrostatic constant)(charge 1)(charge 2) (distance)2 or F  kq1q2 d2 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  106 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: q1  2.0  106 C q2  2.0  106 C d  0.70 m k  9.0  109 N  m2/C2 Solve: F  kq1q2  d2 Unknown: F  ? kq1q2 Original equation: F  2 d 19.0  109 N # m2>C2 2 12.0  106 C 2 12.0  106 C 2 10.70 m 2 2  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  1023 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  1023 N d  0.03 m k  9.0  109 N  m2/C2 Unknown: q  ? kq1q2 Original equation: F  2 d 14  1023 N2 10.03 m 2 2 Fd2 Solve: q1q2    4  1036 C2 k 9.0  109 N # m2>C2 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  1036 C2  2  1018 C Practice Exercises Exercise 1: When sugar is poured from the box into the sugar bowl, the rubbing of sugar grains creates a static electric charge that repels the grains, and causes sugar to go flying out in all directions. If each of two sugar grains acquires a charge of 3.0  1011 C at a separation of 8.0  105 m, with what force will they repel each other? F  kq1q2/d2  (9.0  109 N  m2/C2)(3.0  1011 C)2/(8.0  105 m)2  1.3  103 N Answer: Exercise 2: 1.3  103 N Boppo the clown carries two mylar balloons that rub against a circus elephant, causing the balloons to separate. Each balloon acquires 2.0  107 C of charge. How large is the electric force between them when they are separated by a distance of 0.50 m? F  kq1q2/d2  (9.0  109 N  m2/C2)(2.0  107 C)2/(0.50 m)2  1.4  103 N Answer: Exercise 3: 1.4  103 N Inez uses hairspray on her hair each morning before going to school. The spray spreads out before reaching her hair partly because of the electrostatic charge on the hairspray droplets. If two drops of hairspray repel each other with a force of 9.0  109 N at a distance of 0.070 cm, what is the charge on each of the equally-charged drops of hairspray? q  2Fd2>k  2 19.0  109 N2 17.0  104 m2 2> 19.0  109 N # m2>C2 2  7.0  1013 C Answer: 7.0  1013 C Exercise 4: Bonnie is dusting the house and raises a cloud of dust particles as she wipes across a table. If two 4.0  1014-C pieces of dust exert an electrostatic force of 2.0  1012 N on each other, how far apart are the dust particles at that time? d  2kq1q2>F  2 19.0  109 N # m2>C2 2 14.0  1014 C 2 2> 12.0  1012 N2  2.7  103 m 2.7  103 m Answer: Exercise 5: Each of two hot-air balloons acquires a charge of 3.0  105 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  102 N? d  2kq1q2>F  2 19.0  109 N # m2>C2 2 13.0  105 C 2 2>18.1  102 N2  10. m 10. m Answer: