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# Lec-5 - Previous Lecture The potential of any point a is...

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Previous Lecture The potential of any point a is the work per unit charge to move a test charge from a reference point P to the point a : V a = a P E · d l . The line integral is independent of the path. – p.

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Today V and E Start Chapter 24: Capacitance and Dielectrics – p.
V and E The electric field E determines the potential V : V a = a P E · d l . – p.

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V and E The electric field E determines the potential V : V a = a P E · d l . The potential V determines the electric field E : E = −∇ V – p.
The Gradient Operator means “gradient”: = ˆ i ∂x + ˆ j ∂y + ˆ k ∂z The gradient of V determines E : E = −∇ V = ˆ i ∂V ∂x + ˆ j ∂V ∂y + ˆ k ∂V ∂z . – p.

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The Electric Field E x = ∂V ∂x V ( x + ∆ x, y, z ) V ( x, y, z ) x E y = ∂V ∂y V ( x, y + ∆ y, z ) V ( x, y, z ) y E z = ∂V ∂z V ( x, y, z + ∆ z ) V ( x, y, z ) z – p.
Careful with Conventions Text: If E moves a charge from b to a , considering the work done per unit charge leads to V a

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