In the figure, three thin plastic rods form quarter-circles with a common center of curvature at the origin. The uniform charges on the rods are Q1 = +46 nC, Q2 = 3.0 Q1, and Q3 = -8.0 Q1. What is the net electric potential at the origin due to the rods?
http://www.webassign.net/hrw/hrw7_24-43.gif
http://www.webassign.net/hrw/hrw7_24-43.gif
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The potential at the origin due to one of the quarter-circles is that same as it would be for an equivalent point charge placed at the same distance from the origin, since only the distance and not the direction is important for this calculation.
The potential V due to a number of point charges q¡ at distances r¡ is given by
V = = 1/(4πε۪ ) ∑q¡/r¡ [sum over index i]
with 1/(4πε۪ ) = 8.988e+9 m/F
(This assumes that the potential has been defined as approaching zero as the distance from the charges grows indefinitely large)
Potential V at the origin is then given by
V = 1/(4πε۪ ){Q1/1 + (3×Q1)/2 - (8×Q1)/4}
V = (8.988e+9)(1e-9){46/1 + (3×46)/2 - (8×46)/4}
V = (8.988){46 + 69 - 92}
V = 206.724 volts
The potential V due to a number of point charges q¡ at distances r¡ is given by
V = = 1/(4πε۪ ) ∑q¡/r¡ [sum over index i]
with 1/(4πε۪ ) = 8.988e+9 m/F
(This assumes that the potential has been defined as approaching zero as the distance from the charges grows indefinitely large)
Potential V at the origin is then given by
V = 1/(4πε۪ ){Q1/1 + (3×Q1)/2 - (8×Q1)/4}
V = (8.988e+9)(1e-9){46/1 + (3×46)/2 - (8×46)/4}
V = (8.988){46 + 69 - 92}
V = 206.724 volts