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PPE12_PEPointCharges

# PPE12_PEPointCharges - Potential Potential Energy of Point...

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Potential Potential Potential Energy of Potential Energy of Point Charges Point Charges © RHJansen

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Potential Energy © RHJansen U g = - Γ μ 1 μ 2 ρ U E = κ θ 1 θ 2 ρ The easiest zero point is infinity m 1 m 2 q 1 q 2 r r W g = ∆ - Γ μ 1 μ 2 ρ W E = ∆ κ θ 1 θ 2 ρ
Example 1 © RHJansen Determine the work required to bring a 2.0 μC charge at infinity to a point that is 50 cm from a 4.0 μC charge. W E = ∆ κ θ 1 θ 2 ρ W E = 0.144ϑ W E = κ θ 1 θ 2 ρ - κ θ 1 θ 2 ρ 0 W E = 9 10 9 ( 29 2.0 10 -6 ( 29 4.0 10 -6 ( 29 0.50 ( 29 - 9 10 9 ( 29 2.0 10 -6 ( 29 4.0 10 -6 ( 29 ( 29 W E = 9 10 9 ( 29 2.0 10 -6 ( 29 4.0 10 -6 ( 29 0.50 ( 29 - 0

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Potential Energy of Multiple Charges © RHJansen U E = Σ κ θ ι θ ι ρ Potential energy can be positive or negative. The sign on the charge matters. q 1 q 2 r q 3 r r U E = κ θ 1 θ 2 ρ 12 + κ θ 2 θ 3 ρ 23 + κ θ 1 θ 3 ρ 13 U E = κ θ 1 θ 2 ρ 12 + θ 2 θ 3 ρ 23 + θ 1 θ 3 ρ 13
Example 2 © RHJansen W = Δ E . Subtract initial energy from final energy. q 1 q 2 r q 3 r r q 1 q 2 q 3 2 r 2 r 2 r Three 4 μC charges located at the vertices of an equilateral triangle with sides 20 cm separate so the distance doubles. Determine the work done in this process.

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