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

2. Many Charge Example E = kQ s /r 2 +q o -3q o +4q o -2q o roro What is the force on +4q o ? (direction also) Find the field at +4q o due to the “other” charges. These are the “source” charges. E +q = kQ s /r 2 = k(q o )/(r o ) 2 = E o Direction?Away from + so right E -2q = kQ s /r 2 = k(2q o )/(  2r o ) 2 = E o = k2q o /2(r o ) 2 = k(q o )/(r o ) 2 E -3q = kQ s /r 2 = k(3q o )/(r o ) 2 = 3E o = 3kq o /(r o ) 2

3. Many Charge Example E = kQ s /r 2 +q o -3q o +4q o -2q o roro What is the force on +4q o ? (direction also) E +q = E o E -2q = E o E -3q = 3E o Now add E-Field vectors E x = E +q,x + E -2q,x E x = E o - E o sin45 E x = 0.29E o E y = E -2q,y + E -3q,y E y = E o sin45 + 3E o E y = 3.7E o  = tan -1 (0.29/3.7) = 4.5° E total =  3.7 2 + 0.29 2 E o = 3.71E o F on +4q = (4q o )3.71E o = 14.84q o E o F on +4q = 14.84kq o 2 /r o 2 same direction as E total

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? 2x Stays the same 3 larger 1 larger

5. “Potential Energy Difference” and “Potential Difference” Potential Energy Difference  PE A,B is the change in PE the particular charge feels when it is moved from one location to another. Potential Difference  V A,B is the change in PE a positive 1C charge would feel if it were moved from one location to another.  V A,B = +10 8 Volts, and q = +1  C  PE A,B = +100J  V A,B = -10 8 Volts, and q = +1  C  PE A,B = -100J

6. Which way does the E Field point?  PE A,B = +100J, and q = +1  C What is  V A,B ?  V A,B = 10 8 Volts  V A,B = -10 8 Volts  PE A,B = +100J, and q = -1  C What is  V A,B ? AB Higher Potential E Fields point “downhill” with respect to potential difference E field Remember: From A to B!!!

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

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

10. B A What is the change in potential energy in going from A to B? F E = qE F Hq W AB = qED PE AB = qED PE AB = q  V AB  V AB = ED AB W AB = qED Only applies when the field is uniform over the distance.  V AB ‘s sign depends on the direction of E. In this case it’s positive.