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Coulomb’s Law The force on one charge due to another charge. 𝑟 12 𝑟 12 𝐹 12 q1 q2 𝐹 12 =𝑘 𝑞 1 𝑞 2 𝑟 12 2 𝑟 12

Applied to Continuous Charge Distributions Coulomb’s Law Applied to Continuous Charge Distributions + + + + + + + + + +

Applied to Continuous Charge Distributions Coulomb’s Law Applied to Continuous Charge Distributions Break charge distribution into infinitesimal pieces and sum (integrate) contributions. + + + + + + + + + +

Applied to Continuous Charge Distributions Coulomb’s Law Applied to Continuous Charge Distributions 𝑑 𝐹 𝑑 𝐹 =𝑘 𝑑 𝑞 1 𝑞 2 𝑟 2 𝑟 q2 + 𝑟 + + + + + + + + + dq1

Example: Determine the electric field above the midpoint of a uniform line of charge. λ≡ charge length σ≡ charge area ρ≡ charge volume 𝑑𝑞=λ𝑑𝑥 h λ= 𝑄 𝐿 Q L

Example: Determine the electric field above the midpoint of a uniform line of charge. Q L

Example: Determine the electric field above the midpoint of a uniform line of charge. Q L Determine the electric field due to an infinite line of charge.

Example: Determine the force on a charge in line with a uniform line of charge. q0 Q L d

Example: Determine the electric field above the center of a uniform ring of charge. Q R

Example: Determine the electric force on an electron above the center of a uniform disk of charge. 𝜎 R

Example: Determine the electric force on an electron above an infinite plane of uniform charge.