1. CHAPTER-24
Electric Potential

2. 24-2 Electric Potential Energy
Electric Potential Energy U due to electrostatic force between two or more charges
If electrostatic force does work W on the charges then
U= Uf- Ui=-W
Since electrostatic force is conservative force, W is also path independent
If Ui=0 when particles are at infinity, the U=Uf and W= W
U= Uf= U=-W
Where W is work done in bringing a charge from infinity to the point under consideration

3. Ch 24-2 Electric Potential Energy
Change U in electric potential energy of electron
U= Uf- Ui=-W
But W=qEdcos
Since cos and q are negative , W is positive and U is negative U=-W

4. Ch 24-3 Electric Potential
U depends upon charge q but electric potential V , which is charge independent , given by:
V=U/q
Then V= U/q = -W/q
V= Vf- Vi =-W/q
If particle is initially at infinity then Ui =0 and Vi =0
Then V=Vf =-W /q
Unit of V: Volt(V); 1V=1J/1C
Work done by an Applied Force
Work done in moving a charge q from point I to f in an electric field by applying a force to it.
Then K=W+Wapp
If particle is initially and finally at rest, then
K=0= W+Wapp
Wapp = -W = U =q V

5. Ch 24-4 Equipotential Surfaces
Adjacent points having the same potentials forms Equipotential Surfaces
Equipotential Surfaces are  to E field and field lines
Work done in moving a charge on an Equipotential surface is zero

6. Ch 24-5 Calculating the Potential Difference from the E Field
Work done W on a positive chargeq0 in moving from i to f position
W=F.ds= q0E.ds but q0V=-W
Vf-Vi= -E.ds
If Vi=0, then V= -E.ds
Also V= -E X and
V/X =-E

7. Ch 24-6 Potential due to a Point Charge
Change in electric potential in moving a test positive charge q0 from R to infinity
Vf-Vi= -R E.dr=-kq0R dr/r2
At r=, Vf=0 and at r=R, VR=V then
V= kq0/R
V is a scalar quantity but sign of potential depends upon sign of charge

8. Ch 24-7 Potential due to a Group of Point Charges
The net potential V due to at a point due to a group of point charges
V=Vi= kqi/ri
Net electric potential at P due t o 8 charges = 0 ?

9. Ch 24-10 Calculating the Field from the Potential
Work done in moving a positive test charge between two Equipotential surfaces separated by a distance ds
-q0dV= dW=q0E cos ds
E cos ds=- dV
E cos is component in the direction of ds
Then Ex=-V/x; Ey=-V/y and
Ez=-V/z

10. Ch 24-11 Electrical Potential Energy due to a Group of Point Charges
Work done by an external agent in hold two positive charges distance r apart, is stored as electric potential energy of the two body system and can be recovered by the work done by released charges.
The electric potential energy of a system of fixed point charges is equal to the work that must be by an external agent to assemble the system, bringing each charge in from an infinite distance
U12=Wappl=-W=q2V1 but V1=kq1/r
Then U12= kq1q2/r
For system of 3 charges
Unet= U12+ U23 + U31 etc

11. Ch 24-11 Potential of a Charged Isolated Conductor
An excess charge placed on an isolated conductor will distribute itself on the surface of that conductor so that all points of the conductor –whether on the surface or inside –come to same potential.
Vf-Vi Vf-Vi= -E.ds
Since all points inside the conductor are at E=0
Vf= Vi (Equipotential Surface)

12. Suggested problemsChapter 24