Understanding Electric Fields: Potential, Energy, and Coulomb’s Law Simplified

9: Motion in Fields 9.3 Electrical field, potential and energy

Electric Fields Recap: Coulomb’s law: Electric field strength: F = kQq r2 …the force per unit charge experienced by a small positive point charge placed in the field. E = kQ r2

Electrical Potential It can be shown that... or... Where... V = Electrical potential (Volts or JC-1) r = distance from centre of point charge (m) Q = point charge (Coulombs) k = Coulomb constant = 8.99 x 109 Nm2 C−2 The electrical potential at a point in a field is defined as the work done per unit charge in bringing a positive test charge from infinity to the point in the field. V = kQ r V = 1Q 4πε0 r

E.g. Calculate the potential due to the proton in a hydrogen atom at a distance 0.5 x 10-10m. ( k = 8.99  109 N m2 C-2 ) A: V= 29V

Electric Potential Energy Again it can be shown that... or... The electrical potential energy of a point charge at any point is defined as the work done in moving the charge from infinity to that point. Ep = kQq r Ep = 1Qq 4πε0 r E.g. Calculate the potential energy between the proton in a hydrogen atom and an electron orbiting at radius 0.5 x 10-10m. ( k = 8.99  109 N m2 C-2 ) A: E = -46 x 10-19J

Work done moving a charge If a charge is moved from one point (x) to another (y), where the potential is different, work is done. Work done = Final Ep – Initial Ep = Vyq - Vxq The path taken does not affect the work done. Work done will equal the change in potential energy. x y

Equipotentials Equipotential surfaces also exist in electric fields...

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Potential gradient Again, this will be equal to the field strength at a point in an electrical field... Work done to move a charge from one potential to another = qΔV But also W = FΔx So... FΔx = qΔV So... E = (-) ΔV Δx

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Understanding Electric Fields: Potential, Energy, and Coulomb’s Law Simplified