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Week 5 Solns

# Week 5 Solns - Electromagnetics Workshop Week 5 Coulombs...

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Electromagnetics Workshop – Week 5 Coulomb’s Law and Gauss’s Law Problem 1: Find the total force on the charge q at the origin for the charge configuration shown below. ( 29 ( 29 ( 29 2.5 2 3 3 2 2 0 0 1 1 ˆ ˆ 3 ˆ 4 4 9 y q x q dx dy x y ρ ρ πε πε - - - = + + x y x F l l ( 29 3 0 0 3 2 1 1 1 ˆ ˆ ˆ ˆ 54.1 3.09 10 4 5 3 13 3 10 13 10 q q ρ ρ πε ε - = - - + + - - - × ÷ ÷ F x y x y l l x y q 1 2.5 3 1 2 ρ l ρ l 1

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Electromagnetics Workshop – Week 5 Coulomb’s Law and Gauss’s Law Problem 2: A regular hexagon of charge density ρ l with sides of length s is centered around the origin in the x-y plane. Find the electric field due to this charge on the z -axis. For the top side of the hexagon: ( 29 ( 29 ( 29 2 3 2 2 0 2 2 2 ˆ ˆ ˆ 2 tan 30 4 2tan 30 s s s z x dx s z x ρ πε + - - - ° = + + ÷ ° z x y E l ( 29 2 3 2 2 0 2 2 2 ˆ 4 3 2 3 s s z dx s z x ρ πε + - = + + ÷ z E l [ ] 2 2 2 0 2 2 ˆ V/m 4 3 3 2 2 3 2 3 z s s s s z z ρ πε = + + + ÷ ÷ ÷ z E l , z -component for one side. Since the charge distribution is symmetric about the z-axis, we can just multiply by 6 to get the final answer for the complete hexagon.
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Week 5 Solns - Electromagnetics Workshop Week 5 Coulombs...

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