Electric Potential Energy and Electric Potential Work x y z f - PowerPoint PPT Presentation

Electric Potential Energy and Electric Potential

Work  x y z f f f       Work done W by a force F F dx F dy F dz x y z x y z i i i  x y z f f f       F F dx F dy F dz x y z x y z i i i x y z f f f       F dr F dr F dr x x y y z z y x y z i i i    r  f    Work done W by a force F F d r  r f F r i dr x dr r i F

Potential energy      K K K Work done by electric force F f i E   Work done by other forces F i Static electric is conservati ve, so we can define electric potential energy U as : E    U - Work done by electric force F E E       K - U Work done by other forces F E i y       K U Work done by other forces F i r f F dr x dr r i F

Electric Potential Static E(r) is conservative, the potential difference  V is defined as the negative work done by the force F(r) (which is path independent), divided by the charge (of the test charge).  f   B 1     1 U - F ( r ) d r ` ` i Pay attention to the negative sign   f   U      V - E ( r ) d r 1 A q ` i Unit of electric potential = J/C =V

Warning In the discussion here we will assume electric (force) field is a conservative (force) field. This will not be the case if there is a changing magnetic field. We will come to this point later in the semester.

Potential Difference and Potential If we can define a point Z in space as a point with zero potential, then the potential of all other points in space is defined. Z (V=0 at this point) 1 1 ` `  Z      V at point A - E ( r ) d r A If the problem involves only 1 A potential difference (e.g. ` conservation of energy), the V=? choice of this zero point is not important.

Class 13. Calculation of Electric Potential

Electric potential of a Point Charge This is important because from this we can calculate the potential of any source charge assembly. E Q  V  4 r 0 Q V=0 at r= 

Electric potential of a Constant Field y y=0    V - Ey - y  2 0 V=0 at the sheet of source charges (y=0)

General Observations 1. Electric field tends to point from a high potential point to a low potential point. 2. If you release a test charge particle from rest and let it go along the field line for a short time, the particle will go from a high potential point to a low potential point if it is positive in charge. In reverse, it will go from a low potential point to a high potential point if it is negative in charge.

Calculating Electric Field from Electric Potential Given an electric field, we can calculate the corresponding potential  Z      V at point A - E ( r ) d r A In reverse, given an electric potential, we can calculate the corresponding field:     V V V    ˆ ˆ ˆ E - V - i - j - k    x y z

Calculate the electric potential due to the source charges Electric potential due to a point charge: 1 Q  r V V(r)  E 1 4 r Q 0 Electric potential due to several point charges: V 1 +V 2 +V 3  r 1 1 Q   i r 3 E Q 1 r 2  4 r i 0 i Q 2 Q 3 Electric field due to continuous charge distribution: r 1 dQ     dE V dV  dQ 4 r 0 Note that electric potential is a scalar, it is easier to calculate than electric field (vector).

Calculate Change in Potential Energy If you move a small test charge (so small that it will not affect the charge distribution of the source) of charge q from point i to point f, the change in its potential energy is  U = q (V f – V i ) and now you can use conservation of energy to solve problem:  K +  U = 0