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Lecture 15

# Lecture 15 - PEP112 Spring 2008 Prof Svetlana Malinovskaya...

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PEP112 – Spring 2008 Prof. Svetlana Malinovskaya 5 March 2008 Potential and Field II

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Finding the Potential of a Point Charge • We use the electric field of the point charge to find its electric potential 2 0 2 0 () ( ) 1 4 ( ) 4 r r r r VV V r E d r q E r qd r Vr V r πε 00 11 | 44 r qq rr Δ= = = =∞ + = =
Finding the Electric Field from the Potential Now let’s look at the reverse operation. Figure shows two points separated by small distance, so small that the electric field is essentially constant over this distance. The work done by the electric field as the charge q moves through this small distance is 2 00 0 , ,0 , , 44 4 ss s r UW W F ds qE ds V E s qq Vd V Es E sd s qd V d q q VE E rd r d r r r π επε ε Δ = = Δ === Δ Δ =− Δ → Δ ⎛⎞ = = = ⎜⎟ ⎝⎠

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The Geometry of Potential and Field • Displacement Δ s 1 is tangent to equipotential surface, hence charge moving in this direction experiences no potential difference, and the electric field component along a direction of constant potential is zero. • Displacement Δ s 2 is perpendicular to the equipotential surface. The electric field component is: • The electric field is opposite in the direction to Δ s 2 dV V V E ds s + =− ≈− Δ
The Geometry of the Potential and the Field

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Kirchhoff’s Loop Law • For any path that starts and ends at the same point, we can write that • The sum of all the potential differences encounted while moving around a loop or closed path is zero.
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Lecture 15 - PEP112 Spring 2008 Prof Svetlana Malinovskaya...

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