Electrostatics Electrostatics Smallest bits of electric charge Protons

Electrostatics

Electrostatics Smallest bits of electric charge: – Protons and electrons e = elementary charge (charge on one proton/electron) – = 1. 6 x 10 -19 Coulombs Eg) how many electrons in one coulomb? = 1/e = 6. 2 x 1018 electrons/coulomb Transfer of Charge – charge is transferred when electrons move from place to place “charging by contact”

Electroscope- Charging by induction Explanation: The comb has a negative charge Negative electrons are repelled downwards into the foil leaves The leaves repel each other

H 2 O is polarized! • The polar water molecules orient so that the positive H atoms face the negative comb. The closer surface of the water is negative – attracted to the comb

�Laws of electric charge ◦ Like charges repel, unlike charges attract Note: charged objects attract neutral ones ◦ A negative object pushes electrons away from the surface, thus creating a net positive object: “charging by induction” Negative object Neutral object HW (discuss): pg. 491 # 1 -10

Coulomb’s Law “Like charges repel, unlike charges attract” q 1 d q 2 Point charges q = amount of charge in coulombs Magnitude of Force: F = K q 1 • q 2 d 2 K = 9. 0 x 109 Nm 2/C 2 “coulomb’s constant”

Ex: An electron orbits a proton at a distance of 2. 0 x 10 -11 m. Find: a) The force of attraction b) The orbital period e Note: e = 1. 6 x 10 -19 C me = 9. 11 x 10 -31 Kg a) b)

Ex 2. A small plastic sphere has a known charge of +6. 5 µC. It is attracted to a second small sphere 3. 5 cm away with a force of 0. 0023 N. Find: a) The charge on the second sphere b) The number of excess electrons a) = 4. 8 x 10 -11 C negative! b) = 3. 0 x 108 electrons

Principle of Superposition The resultant force on any one particle equals the vector sum of all forces. Eg: Find: a) the net force on the – 5. 0 C charge b) Where should that -5. 0 charge be placed so that the net force is zero? 2. 0 C -1. 0 C _ + 2 m _ 2 m Q 1 Q 2 a) F = F 1 – F 2 Q 5 _ F 2 -5. 0 C F 1 Q 5

b) 2. 0 C + -1. 0 C -5. 0 C _ _ x 2 m Q 1 Q 2 Q 5 _ F 2 F 1

Electrostatics in 2 -D eg) Three +20µC charges are placed at the corners of an equilateral triangle of side 1. 0 m. Find the force exerted on one charge by they other two. + F 1 F + + x 30 o F 2 F 1 = F 2 = K(20 x 10 -6)2 1. 02 = 3. 6 N F = 2 x F 1 x = 2 x F 1 cos 30 = 6. 2 N

2) 4 charges of magnitude 10µC are placed at the corners of a square of side 2. 0 m. Find the force exerted on one by the other three. 1 y + 2 F 3 F 2 F + + + 3 x F 1 -6)2 K(10 x 10 F 3 = F 1 = = 0. 225 N 2 2. 0 -6)2 K(10 x 10 F 2 = = 0. 1125 N 8 F = 2 x F 1 cos 45 + F 2 = 2(. 225)cos 45 +. 1125 = 0. 43 N

Fc Q (a) + db Q + (b) Q + 5 m 2 m + (c) Q Fb Fa 3) Find the force on the top right charge. Q = 40µC db = √(22 + 52) = √ 29 θ = tan-1(2/5) = 21. 8 o X : Fx = Fa + Fbcosθ HW (AP) 2 2 KQ KQ = d 2 + d 2 cosθ a b P 492: 1 1 2 = KQ ( 2 + cos 21. 8) 5 29 1, 3, 4, 6 -10 = 1. 04 N P 493: Y : Fy = Fc + Fbsinθ 1 sin 21. 8) = KQ 2( 122 + 29 12 -15, 17 -20 = 3. 78 N F = √(1. 0422 + 3. 7822) = 3. 9 N F θ = tan-1(1. 04/3. 78) = 15 o 3. 9 N, 15 o with vertical