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Today 2/21

Today 2/21. E-Field and Coulomb’s Law 18.4-5 Examples HW: “2/21 2-D E Field ” Due Wednesday 2/26. q 1. k Q s. k Q s. k 6 q o. k 2 q o. 1. 1. kq o. kq o. r 2. r 2. (4 r o ) 2. (6 r o ) 2. 6. 8. r o 2. r o 2. 4. kq o 2. 24. r o 2. 1. 1. kq o. 1. kq o. 6. 8. r o 2.

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Today 2/21

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  1. Today 2/21 • E-Field and Coulomb’s Law 18.4-5 • Examples • HW: “2/21 2-D E Field ” Due Wednesday 2/26

  2. q1 k Qs k Qs k 6qo k 2qo 1 1 kqo kqo r2 r2 (4ro)2 (6ro)2 6 8 ro2 ro2 4 kqo2 24 ro2 1 1 kqo 1 kqo 6 8 ro2 24 ro2 E = kQs /r2 Many Charge Example (Like HW) Each Square is ro on a side, Q1 = -4qo, Q2 = +2qo, Q3 = -6qo (See how this simplifies the math) Q1 Find the E field at Q1’s location. Up, (away from Q2) EQ2,x = Q2 EQ3,x = Down, (toward Q3) Q3 FOthers,q1 = q1Enet,x Add vectors to get Enet,x Down at the x

  3. q2 k Qs k Qs k 6qo k 4qo 3 1 kqo kqo r2 r2 (4ro)2 (2ro)2 4 2 ro2 ro2 5 kqo2 2 ro2 3 1 kqo 5 kqo 2 4 ro2 4 ro2 E = kQs /r2 Many Charge Example (Like HW) Each Square is ro on a side, Q1 = -4qo, Q2 = +2qo, Q3 = -6qo (See how this simplifies the math) Q1 Find the E field at Q2’s location. Up, (toward Q1) EQ1,x = Q2 EQ3,x = Down, (toward Q3) Q3 FOthers,q2 = q2Enet,x Add vectors to get Enet,x Down at the x

  4. = k(2qo)/(2ro)2 E = kQs /r2 Many Charge Example What is the force on +4qo? (direction also) +qo +4qo Find the field at +4qo due to the “other” charges. These are the “source” charges. ro E+q = kQs/r2 = k(qo)/(ro)2 = Eo -2qo -3qo Direction? Away from + so right E-2q = kQs/r2 = k2qo/2(ro)2 = k(qo)/(ro)2 = Eo E-3q = kQs/r2 = k(3qo)/(ro)2 = 3kqo/(ro)2 = 3Eo

  5. Etotal = 3.72 + 0.292 Eo E = kQs /r2 Many Charge Example What is the force on +4qo? (direction also) +qo +4qo E+q = Eo E-2q = Eo E-3q = 3Eo ro Now add E-Field vectors -2qo Ex = E+q,x + E-2q,x -3qo Ex = Eo - Eosin45 Ey = E-2q,y + E-3q,y Ex = 0.29Eo Ey = Eosin45 + 3Eo  = tan-1(0.29/3.7) = 4.5° Ey = 3.7Eo Fon +4q = (4qo)3.71Eo = 14.84qoEo = 3.71Eo Fon +4q = 14.84kqo2/ro2 same direction as Etotal

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