Recall Gravitational PERecall Gravitational PE The work done to lift a ball of mass 1 kg a The work done to lift a ball of mass 1 kg a

vertical height of 1 m is 10 Jvertical height of 1 m is 10 J

What is the work done to lift 5 bowling What is the work done to lift 5 bowling balls?balls?

Work done for total job vs. Work done for total job vs. work done work done per ballper ball

The work done to lift one ball is 10 The work done to lift one ball is 10 J, and the work done to lift five is J, and the work done to lift five is 50 J. The work done per ball 50 J. The work done per ball remains 10 J.remains 10 J.

Electrical PEElectrical PE Assume that it takes 10 J to lift one positive charge Assume that it takes 10 J to lift one positive charge

“up” from a negative plate to a positive plate“up” from a negative plate to a positive plate

How much will it take to “lift” 5 charges How much will it take to “lift” 5 charges from the negative plate to the positive from the negative plate to the positive plate?plate?

Work done for total job vs. Work done for total job vs. work done work done per chargeper charge

The work done to lift one The work done to lift one charge is 10 J, and the charge is 10 J, and the work done to lift five is work done to lift five is 50 J. The work done per 50 J. The work done per charge remains 10 J.charge remains 10 J.

The electrical PE is the The electrical PE is the total work donetotal work done

The The electrical potentialelectrical potential is the is the work done per work done per chargecharge (measured in J/C (measured in J/C or volts (V))or volts (V))

qWV

Which is more dangerous?Which is more dangerous?

1 x 10-6 C at 300,000 V

150,000 C at 12 V

Recall: Gravitational PERecall: Gravitational PE When in a uniform field, UWhen in a uniform field, Ugg=mgh=mgh In a changing field (such as around planet), In a changing field (such as around planet),

rGmMU g

Electrical PotentialElectrical Potential When in a uniform E-field, V=W/q=EdWhen in a uniform E-field, V=W/q=Ed In a changing field (such as that In a changing field (such as that

around a point charge),around a point charge),

rkQ

qUV E

Adding potentialsAdding potentials The total potential at a point near many point The total potential at a point near many point

charges is the numerical sum of the contribution charges is the numerical sum of the contribution from each charge. Potential is NOT a vector.from each charge. Potential is NOT a vector.

Equipotential linesEquipotential lines

EquipotentiEquipotential lines are al lines are like the like the lines on a lines on a contour or contour or topographic topographic map – they map – they represent represent levels of levels of constant constant potentialpotential

Equipotential lines, cont.Equipotential lines, cont. No work is done to move along an No work is done to move along an

equipotential line or curveequipotential line or curve Equipotential lines (curves) are Equipotential lines (curves) are

always perpendicular to E-field always perpendicular to E-field lineslines

Relationship between E Relationship between E and Vand V

drdUF

drdVE

The magnitude of the E-field is The magnitude of the E-field is given by the gradient of the given by the gradient of the potentialpotential