L17_a - r Getting Electric Field E from Electric Potential...

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Getting Electric Field E r from Electric Potential V (IMPORTANT) Useful because V is a scalar and superposition does not require vector sum Start by noting: = B A s d E V r r implies s d E dV r r = E r due to a point charge (radial electric field) only nonzero term in s d E r r is dr E radial So: dr E s d E dV radial = = r r Implies: dr dV E = radial Check: 2 e e r q k r q k dr d = (as it should be)
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Can get components of E r from derivatives of V Start with: k E j E i E E z y x ˆ ˆ ˆ + + = r and k dz j dy i dx s d ˆ ˆ ˆ + + = r Then: [ ] dz E dy E dx E s d E dV z y x + + = = r r Implies: dx dV E x = dy dV E y = dz dV E z = Components of E r are nonzero only for directions along which V changing If V is constant over some surface (i.e. an equipotential): o E r has no components along that surface Says: E r is always perpendicular to equipotential surfaces
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This note was uploaded on 03/08/2012 for the course PHYSICS 1051 taught by Professor Michaelmorrow during the Winter '12 term at Memorial University.

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L17_a - r Getting Electric Field E from Electric Potential...

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