Electrical Energy and Potential Difference

When two charges interact, there is a force between them When two charges interact, there is a force between them. This force creates potential energy. This electric PE is a form of mechanical energy, like KE, GPE and PEelastic

- - Charges moving in a uniform electric field + + A + charge moving against the electric field gains PE A + charge moving with the electric field loses PE A - charge moving against the electric field loses PE A - charge moving with the electric field gains PE

DPEelectric = -qEDd Measured in Joules Dd is in the direction of the electric field

Electrical Potential Energy for a pair of charges

Electric Potential is the amount of PEelectric divided by the amount of charge Potential Difference is the change in V

Potential Difference is measured in Volts (V), which equals 1 J/C It can also be expressed as DV = -EDd or DV = kCq/r or DV = W/q

Sample Problems A uniform electric field is directed in the + x direction at 250 N/C. A 12mC charge moves from the origin to the point (20.0 cm, 50.0 cm). What is the change in PE? Given DPEelectric = -qEDd q = 12 x 10-6 C = (-12 x 10-6 C)(250 N/C)(.200 m) moving with field, so will lose PE = -6.0 x 10-4 J E = 250 N/C d = .200 m

A proton is released from rest in a uniform electric field of 8 A proton is released from rest in a uniform electric field of 8.0 x 104 V/m and moves .50 m. Find the potential difference and DPE for these positions. Given a) DV = -EDd E = 8.0 x 104 V/m DV = -(8.0 x 104 V/m)(.5 m) d = .5 m DV = -4.0 x 104 V b) DPE = DVq q = 1.60 x 10-19 C DPE = (-4.0 x 104 V)(1.60 x 10-19 C) DPE = -6.4 x 10-15 J