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Lecture 11 - Equipotentials

# Lecture 11 - Equipotentials - Example Getting the electric...

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1 Lecture 11 More Example of Electric Potential. Equipotentials. Lightning rods and why you lose your radio station inside tunnels. Example: Getting the electric field from the electric potential   E V We saw last time that   2 2 ( , , ) 2 5 4 V x y z x xz y z Example: Find the electric field for ˆ ˆ ˆ 2 5 2( 4 ) E x z i j x z k   2 2 x V E x z x     5 y V E y     2 8 z V E x z z 30 V 20 V 10 V E Equipotentials Equipotentials for a positive point charge Topographic map of Mt. Fuji 30 V 20 V 10 V V 2D mapping of potential: E Equipotentials for a positive point charge x y E

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2 X A X B Take two points A and B on an equipotential surface For any path between A and B on the surface, A B 0 B A V V E dl   The electric field is always perpendicular to equipotential surfaces must be perpendicular to E dl -1000 -500 -250 500 250 1000 The figure below looks (more or less) like the equipotentials of: A. Two identical 100 -100 ACT: Equipotentials -2500 2500 It is actually an electric fish! charges B. A dipole C. Two charges of equal sign but different magnitude -250 250 The electric field points in the direction of decreasing potential and is perpendicular to the equipotential surfaces: -2500 -1000 -500 500 1000 2500 + Black ghost knife fish This fish uses the electric field to detect approaching preys or enemies. Changes in the
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