10:19.pdf

# 10:19.pdf

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E from V & V from E. Lecture 9.

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Calculate V from E: Calculate the potential from a charged conducting sphere R Q
Potential from Planes of charge σ > 0 σ - σ x 0 L

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Potential from Planes of charge σ > 0 σ x 0 a b conductor

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Practice with the gradient: V to E Compute the E field: V ( ~ r ) = Q 4 ⇡✏ 0 r V ( ~ r ) = A x + B y + C z

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Gradient (in different coordinates) Cartesian: Spherical: Cylindrical: ~ r ⌘ ˆ x @ @ x + ˆ y @ @ y + ˆ z @ @ z ~ r ⌘ ˆ r @ @ r + ˆ φ 1 r @ + ˆ z @ @ z ~ r ⌘ ˆ r @ @ r + ˆ 1 r @ @✓ + ˆ φ 1 r sin @
Question from FlipIt Physics: Is there a connection between field lines and electric potential (energy) ? Yes… let’s talk about that now!

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Visualizing the potential: Equipotential Surfaces Normal to E field/lines Spacing 1/E
Examples of Equipotential Surfaces: What is the charge distribution?

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Example from the

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