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Today5/2 Questions? E-Fields and Potential Difference (review) E = kQs /r2 Many Charge Example +qo -2qo +4qo -3qo What is the force on +4qo? (direction also) 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 Direction? Away from + so right E-2q = kQs/r2 = k(2qo)/(2ro)2 = k2qo/2(ro)2= k(qo)/(ro)2 = Eo E-3q = kQs/r2 = k(3qo)/(ro)2 = 3kqo/(ro)2 = 3Eo E = kQs /r2 Many Charge Example +qo +4qo What is the force on +4qo? (direction also) E+q = Eo E-2q = Eo E-3q = 3Eo ro Now add E-Field vectors -2qo -3qo Ey = E-2q,y + E-3q,y Ey = Eosin45 + 3Eo Ex = E+q,x + E-2q,x Ex = Eo - Eosin45 Ex = 0.29Eo = tan-1(0.29/3.7) = 4.5° Ey = 3.7Eo Fon +4q = (4qo)3.71Eo = 14.84qoEo Etotal = 3.72 + 0.292 Eo = 3.71Eo Fon +4q = 14.84kqo2/ro2 same direction as Etotal 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 1 larger b. 2 and 3 3 larger The test charge is doubled when at 2 a. how does the force change? 2x b. how does the electric field change? Stays the same “Potential Energy Difference” and “Potential Difference” Potential Energy Difference PEA,B is the change in PE the particular charge feels when it is moved from one location to another. Potential Difference VA,B is the change in PE a positive 1C charge would feel if it were moved from one location to another. VA,B = +108 Volts, and q = +1C PEA,B = +100J VA,B = -108 Volts, and q = +1C PEA,B = -100J Which way does the E Field point? PEA,B = +100J, and q = +1C What is VA,B? Remember: From A to B!!! VA,B = 108 Volts Higher Potential E field A Higher Potential B PEA,B = E field +100J, and q = VA,B = -108 Volts -1C What is VA,B ? “downhill” with respect to potential difference E Fields point 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 Energy stored kQ V r PE qV V 0 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 3m the work required to assemble the charges. 4m 5m Move them all very far away, bring them in one at a time, and total up the work done. Enet = 0 How big is E? E 2 0 (+) E 2 0 E net Enet = 0 (-) 0 WAB = qED What is the change in potential energy in going from A to B? PEAB = qED PEAB = qVAB VAB = EDAB WAB = qED FHq B FE = qE A Only applies when the field is uniform over the distance. VAB‘s sign depends on the direction of E. In this case it’s positive.