As You Come In… Write the equation for the potential difference comparing a test mass “m” at a point “A” to a test mass “m” at a point “B”.

Electrical Potential Consider the following diagram: – Uniform electrical field “E” – Equipotential lines– same potential along dotted lines – Test charge with charge “q” Electrical Field “E” q

Aside: Test Charge “q” Electric charge- object’s ability to interact with an electric and/or magnetic field – Symbol: q (or Q) – SI unit: Coulomb (C) – Can be either positive (+) or negative (-) – Test charges will be (-) Charles-Augustin de Coulomb Image obtained from:

Electrical Potential Moving test charge “q” – Moving from A to B No work/energy required—why? “q” has same potential at A as it does at B q A B Electrical Field “E”

Force needed to keep “q” at equipotential line is perpendicular to displacement Recall: W = ǁFǁǁsǁcos(δ) What is F equal to? F = -qE Electrical Potential q A B F s so W = 0 J Electrical Field “E”

Electrical Potential – Moving from A to C Will take work or energy– why? “q” has different potential at C than at A q A B C Electrical Field “E”

Electrical Potential Force needed to move “q” to new equipotential line is parallel to displacement Recall: W = ǁFǁǁsǁcos(δ) What is F equal to? F = -qE q A B C so W = Fs F s Electrical Field “E”

dAdA Electrical Potential Finding s: – Set d = 0 m line – d A and d C : distance to points A and C respectively – s = d C - d A – W = Fs = qE(d C - d A ) – W = qEd C - qEd A – What must qEd be? q A B C F s d = 0 m dCdC Electrical Field “E”

dAdA Electrical Potential – W = EPE C - EPE A – W = ΔEPE ΔEPE: change in electrical potential energy q A B C F s d = 0 m dCdC Electrical Field “E”

Electrical Potential q A B C d = 0 m Electrical Field “E”

Electrical Potential q A B C d = 0 m Low E. Pot. High E. Pot. Electrical Field “E”

(Electrical) Potential Difference q A B C d = 0 m Electrical Field “E” Low E. Pot. High E. Pot.

(Electrical) Potential Difference q A B C dAdA d = 0 m dBdB Electrical Field “E” Low E. Pot. High E. Pot.

Voltage q A B C V = 0 V (ground) Electrical Field “E” Low Voltage High Voltage

Electrical Fields q A B C V = 0 V (ground) Electrical Field “E” Low Voltage High Voltage

Electrical Fields q A B C V = 0 V (ground) Electrical Field “E” Low Voltage High Voltage ? ? ?

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