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# lecture09 - Physics for Scientists Engineers 2 Chapter 23 1...

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9/15/11 Physics for Scientists & Engineers 2, Chapter 23 1

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September 15, 2011 Physics for Scientists&Engineers 2 2 Given is a uniform electric eld E. Find the potential di ff erence V f -V i by moving a test charge q 0 along the path icf. Idea: Integrate along the path connecting ic and cf. Imagine, we move a test charge q 0 from i to c and from c to f. i f c
September 15, 2011 Physics for Scientists&Engineers 2 3 Given is a uniform electric eld E. Find the potential di ff erence V f -V i by moving a test charge q 0 along the path icf. Along ic, ds and E are perpendicular i f c With the distance from c to f: d/sin(45 o )

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September 15, 2011 Physics for Scientists&Engineers 2 4 We just derived V f -V i for the situation b). What is V f -V i when going directly from i to f without stopping by c? A: 0 B: -Ed C: +Ed D: -1/2 Ed i f c i f a) b)
9/15/11 Physics for Scientists & Engineers 2, Chapter 23 6 We calculate the electric potential from a system of n point charges by adding the potential functions from each charge is summation produces an electric potential at all points in space – a scalar function Calculating the electric potential from a group of point charges is usually much simpler than calculating the electric eld It’s a scalar V = V i i = 1 n = kq i r i i = 1 n

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9/15/11 Physics for Scientists & Engineers 2, Chapter 23 7 Assume we have a system of three point charges: q 1 = +1.50 μ C q 2 = +2.50 μ C q 3 = -3.50 μ C q 1 is located at (0, a ) q 2 is located at (0,0) q 3 is located at ( b ,0) a = 8.00 m and b = 6.00 m. What is the electric potential at point P located at ( b , a )?
9/15/11 Physics for Scientists & Engineers 2, Chapter 23 8 e electric potential at point P is given by the sum of the electric potential from the three charges V = kq i r i i = 1 3 = k q 1 r 1 + q 2 r 2 + q 3 r 3 = k q 1 b + q 2 a 2 + b 2 + q 3 a V = 8.99 10 9 N m 2 C 2 1.50 10 6 C 6.00 m + 2.50 10 6 C 8.00 m ( ) 2 + 6.00 m ( ) 2 +

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lecture09 - Physics for Scientists Engineers 2 Chapter 23 1...

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