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Chapter 23--Examples
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Problem In the figure below, point P is at the center of the rectangle. With V=0 at infinity, what is the net electric potential at P due to the six charged particles? -2q +3q +5q -3q P d
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Find distance from corners to P
-2q +3q +5q -3q P d s d/2
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Potentials (Voltage) is a scalar
2 3 1 -2q +3q +5q -3q P d s d/2 4 5 6
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Problem A charge q is distributed uniformly throughout a spherical volume of radius, R. Setting V=0 at infinity shown that the potential at a distance r from the center, where r<R is given by What is the potential difference between a point on the surface and the sphere’s center?
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First, use Gauss’s law to find the E-field inside and outside the sphere
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Outside is simpler
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Inside
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Voltage=Outside+Inside
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Part b) What is the potential difference between a point on the surface and the sphere’s center?
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Okay, that is if V=0 at infinity what if V=0 at the center of the sphere?
Same as previous Same as previous
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Problem The electric potential at points in a space are given by
V=2x2-3y2+5z3 What is the magnitude and direction of the electric field at the point (3,2,-1)?
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E=-grad(V)
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Directions Direction w.r.t +x axis Direction w.r.t +z axis
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Problem Three C charges form an equilateral triangle, 1.7 m on a side. Using energy that is supplied at a rate of 0.83 kW, how many days would be required to move one of the charges to the midpoint of the line joining the other two charges?
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Draw It Initially, this charge is 1.7 m from the other two charges
Finally, this charge is 0.85 m from the other two charges
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Potential Difference
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Potential Energy
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Power=Work per unit time
P=W/Dt W=-DU So 0.83 kW= 830 J/s And Dt= DU/P=152x106/830 Dt=183,699 s or 51 hours or 2.12 days
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