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Today5/2

Today5/2. Questions? E-Fields and Potential Difference (review). = k(2q o )/( 2 r o ) 2. E = kQ s /r 2. Many Charge Example. What is the force on +4q o ? (direction also). +q o. +4q o. Find the field at +4q o due to the “other” charges. These are the “source” charges. r o.

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Today5/2

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  1. Today5/2 • Questions? • E-Fields and Potential Difference (review)

  2. = 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

  3. 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

  4. What direction would the force point on a small positive charge at 1,2,3? • Compare the size of the force exerted on a small charge at • a. 1 and 2 • b. 2 and 3 • The test charge is doubled when at 2 • a. how does the force change? • b. how does the electric field change? 1 larger 3 larger 2x Stays the same

  5. “Potential Energy Difference” and “Potential Difference” Potential Energy DifferencePEA,Bis the change in PE the particularcharge feels when it is moved from one location to another. Potential DifferenceVA,B is the change in PE a positive 1C charge would feelifit were moved from one location to another. VA,B = +108 Volts, and q = +1C VA,B = -108 Volts, and q = +1C PEA,B = +100J PEA,B = -100J

  6. E field Remember:From A to B!!! PEA,B = +100J, and q = -1C What is VA,B? E field Which way does the E Field point? PEA,B = +100J, and q = +1C What is VA,B? VA,B = 108 Volts Higher Potential A B Higher Potential VA,B = -108 Volts E Fields point “downhill” with respect to potential difference

  7. At which location is the potential highest? At 2 downhill to 1 and 3 At which location is the potential lowest? At 3 uphill to 1 and 2

  8. Energy stored How much energy is stored in the assembly of charges? All are +1 x 10-3C and 1g (1 x 10-3kg). Energy stored is the same as the work required to assemble the charges. 3m 4m Move them all very far away, bring them in one at a time, and total up the work done. 5m

  9. (-) Enet = 0 Enet = 0 How big is E? (+)

  10. WAB = qED FHq FE = qE WAB = qED What is the change in potential energy in going from A to B? A B Only applies when the field is uniform over the distance. DVAB‘s sign depends on the direction of E. In this case it’s positive. PEAB = qED PEAB = qDVAB DVAB = EDAB

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