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

Electric Potential Energy and Electric Potential

Work

dz F dy F dx F F

z z z y y y x x x

f i f i f i

  

   

Work done W by a force

r d F F dr F dr F dr F dz F dy F dx F F

f i f i f i f i f i f i f i

r r z z z z y y y y x x x x z z z y y y x x x

   

 

       

      

Work done W by a force

F

x y ri rf

dr F dr

Potential energy

i i E E E E i E i f

F forces

• ther

by done Work U K F forces

• ther

by done Work U

• K

F force electric by done Work

• U

: as energy U potential electric define can we so ve, conservati is electric Static F forces

• ther

by done Work F force electric by done Work K K K                      

F

x y ri rf

dr F dr

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).

Electric Potential A B1

` 1 ` 1 `

r d ) r ( F

• U

f i

     



Pay attention to the negative sign

r d ) r ( E

• q

U V

f 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 A Z (V=0 at this point)

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.

1 ` 1 ` 1 `

r d ) r ( E

• A

point at V

Z A

     

V=?

If the problem involves only potential difference (e.g. conservation of energy), the 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.

Q E

r 4 Q V   V=0 at r=

Electric potential of a Constant Field

V=0 at the sheet of source charges (y=0) y 2

• Ey
• V

   

y 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

r d ) r ( E

• A

point at V

Z A

     

In reverse, given an electric potential, we can calculate the corresponding field:

k ˆ z V

• j

ˆ y V

• i

ˆ x V

• V
• E

         

Calculate the electric potential due to the source charges Electric potential due to a point charge:

r Q 4 1 V  

Electric potential due to several point charges:

r Q 4 1 E

i i i





 

Electric field due to continuous charge distribution:

r dQ 4 1 dV V 

 

 

Q Q1 E1 Q2 Q3 r r1 r2 r3 r dQ dE V(r) V1+V2+V3 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 – Vi) and now you can use conservation of energy to solve problem: K + U = 0