Coulomb's Law - Berkner's Base for Physics and Math

Forces and Fields Lesson 4 Charles Coulomb 1736 -1806 Discovered the inverse square law which states that as you move charges apart the force between them decreases 1 exponentially Fe r 2 Also showed that the force between two charged objects is proportional to the product of the charges Fe q1q2 Unit of electrical charge is named after him The Torsion Balance

Coulomb used a torsion balance (Physics 20 universal gravitational constant) to determine k a universal value called Coulombs Constant. http://www.youtub e.com/watch?v=_5 VpIje-R54 By measuring the amount of twist when the charges repelled each other, the force could be measured and the constant could be determined. Coulombs Law describes the electrostatic forces between two charged objects.

Where: kq1q2 Fe 2 r Fe is the electrostatic force k is Coulombs Constant 2 N m (8.99 10 ) 2 q is the charge in Coulombs (C) C 9 ( the unit for charge is 1 C which equals the charge of 18

6.25 10 electrons ) r is the distance separating the two charges (m) Notice the similarities to Newtons Law of Universal Gravitation Gm1m2 Fg 2 r This shows only attraction while Coulombs Law can be used for both attractive and repulsive situations Gravity is a weak force requiring large masses Electric forces are very large in comparison and are effective with small charges Using

Coulombs Law (1 D) To calculate the electric force between two charges, always solve for the absolute value and ignore the sign on the charge. Determine whether the charges attract or repel at the end. ( A point charge is a small + or charge.) Eg) Calculate the magnitude of the electric force between two point charges of +4.00 uC and +3.00 uC when they are 4.50 cm apart. r 0.045m q1 4.00 C q2 3.00 C kq1 q2 Fe 2 r N m 2 6

6 (8.99 10 )(4.00 10 C )(3.00 10 C) 2 C Fe (0.045m) 2 53.27 N 9 The magnitude of the repulsive force is 53.3N . Eg 2) A comb with 2.0 uC of charge is 1.5 m to the left from a hair with -3.0 uC of charge. Determine

the force the hair exerts on the comb. r 1.5m q1 2.0 C kq1q2 Fe 2 r q2 3.0 C 2 N m 6 6 (8.99 109 )(2.0 10 C )(3.0

10 C) 2 C Fe (1.5m) 2 2.4 10 2 N The hair is pulling the comb with a force 2 of 2.4 10 N right. 6 Two point charges1.8 10 C of 6 2.4and 10 C

3 produce a force of10 N 2.2 on each other. How far apart are these two kq1q2 charges?Fe 2 r kq1q2 r Fe 2 N m 6 6 (8.99 109 )(1.8 10 C )(2.4

10 C) 2 C r 2.2 10 3 N 4.2m NOTE: Charges are usually in the range of microCoulombs. Only lightning strikes have a charge of 1 or 2 coulombs. The electrons charge is so important it is called an elementary charge. Its symbol is e and is also on your formula sheet. Net electrical force Determine the net force on object B. always interpret this to mean that the

object in question is free to move and the other objects are stationary. Forces on B Free body diagram F C on B kq1q2 Fe 2 r 8.99 109 N m 2 / C 2 1.00C 2.00C Fe 2 (1.00m) 10 Fe 1.798 10 N [left ] F A on B kq1q2 Fe 2 r 8.99 109 N m 2 / C 2 3.00C 2.00C

Fe 2 (2.00m) 10 Fe 1.3485 10 N [right ] Fnet Fnet FC on B FAon B 10 10 Fnet 1.798 10 N 1.3485 10 N 9 Fe 4.50 10 N [left ] Example: Find the net electrical force on B.

A 2.0 x 10 -6 C 3.20 m -1.5 C B -3.8 C AB 4.1 m C k q1 q2 Fe 2 r 2 9 Nm

6 6 8.99 10 2 10 C 3.8 10 C 2 C Fe 2 3.2 m Fe 6.67 10 3 N

down on B * BC F kq1q2 e 2 r 2 Nm 9 6 6 8.99 10 3.8 10 C 1.5 10 C 2

C Fe 2 4.1 m 3 Fe 3.05 10 N left on B * 3.05 x 10 -3 N Draw Vector Diagram 6.67 x 10 -3 N FR 3.05 10 3 2 6.67 10 3 FResultant

2 FR 7.3 10 3 N O 6.67 10 3 N tan A 3.05 10 3 N 65 3 FR 7.3 10 N , W 65 S * Example: Calculate the gravitational force between an electron and a proton placed 1.0 cm apart. G m1 m2 Fg R2 2 11 Nm

31 27 1.0 10 9 . 11 10 kg 1 . 67 10 kg 2 kg Fg 1.0 10 2 m 2

Fg 1.0 10 63 N * Example: Calculate the electrical force between an electron and a proton placed 1.0 cm apart. kq1q2 Fe 2 r Nm Felectrical 2

8.99 10 9 1.6 10 19C 1.6 10 19C 2 C 1.0 10 2 m 2

Felectrical 2.3 10 24 N 2.3 10 24 N electrical force 10 ratio : 63 gravitational force 1.0 10 N 39 times * Three point charges, A, B, and C, are arranged in a line as shown. a.

Determine the net electrostatic force acting on charge B. b. The charge on object C is negative. Identify the sign of the charge (+ or -) on object i. A. ii. B. 2 D Example: Three point charged objects are arranged in a right angle as shown in the diagram. a. The charge on object A is positive. Identify the sign of the charge (+ or -) on object i. B. (negative) ii. C. (negative) b. Determine the net electrostatic force acting on charge B. Read WB p. 85-86 TB p. 532-6

Examples 10.3 to 10.6 Do WB p.87 2-5,8,10,14,16,18,19

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