curl_4 - equal to the potential energy per unit charge ...

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PHY2061 R. D. Field Department of Physics curl_4.doc Univesity of Florida Curl of the Electrostatic Field The electrostatic field r r KQ E ! ! 3 = is a radial ( or central ) function of r. It points radially outward (or inward) along the radius vector z z y y x x r ˆ ˆ ˆ + + = ! and has a magnitude E that depends only on the distance 2 2 2 z y x r + + = from the origin. Thus 0 = × E ! ! This means that the electrostatic field can be written as the gradient of a scalar function V as follows: V E = ! ! The electric potential V(x,y,z) is a scalar function of position and is
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Unformatted text preview: equal to the potential energy per unit charge. ∫ ⋅ − = − = ∇ P P r d E P V P V V ) ( ) ( ! ! . P is some reference point and V(P ) is the potential at the reference point. Electric Potential of a Point Charge: ) ( ˆ ) ( 2 P V r d r r KQ P V P P + ⋅ − = ∫ ! Taking P = infinity and V(P ) = 0 gives r KQ r V = ) ( Electrostatic Field Electric Potential r E Q P P Curve C Point Charge...
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