**Electric Potential Energy**

**ΔU=-W**

Where ΔU = Change in Potential energy

W= Workdone by the electric lines of forces

For a system of two particles

U(r)=q

_{1}q

_{2}/4πεr

where r is the seperation between the charges

We assume U to be zero at infinity

Similarliy for a system of n charges

U=Sum of potential energy of all the distinct pairs in the system

For example for three charges

U=(1/4πε)(q

_{1}q

_{2}/r

_{12}+q

_{2}q

_{3}/r

_{23}+q

_{1}q

_{3}/r

_{13})

Another way to represent

U=1/2ΣqV

where V is the potential at charge q due to all the remaining charges

Electric Potential:

Just liken Electric field intensity is used to define the electric field,we can also use Electric Potential to define the field

Potential at any point P is equal to th workdone per unit test charge by the external agent in moving the test charge from the refrence point(without Change in KE)

V

_{p}=W

_{ext}/q

So for a point charge

V

_{p}=Q/4πεr

where r is the distance of the point from charge

**Some points about Electric potential**1. It is scalar quantity

2.Potential at point due to system of charges will be obtained by the summation of potential of each charge at that point

V=V

_{1}+V

_{2}+V

_{3}+V

_{4}

3.Electric forces are conservative force so workdone by the electric force between two point is independent of the path taken

4. V

_{2}-V

_{1}=-∫ E.dr

5 In cartesion coordinates system

E=E

_{x}i+E

_{y}j+E

_{z}k

dr=dxi+dyj+dzk

Now

dV=-E.dr

So dv=-(E

_{x}dx+E

_{y}dy+E

_{z}dz)

So E

_{x}=∂V/∂x

Similary

E

_{y}=∂V/∂y and E

_{z}=∂V/∂z

Also

E=-[(∂V/∂x)i+(∂V/∂y)j+(∂V/∂z)k]

4

Surface where electric potential is same everywhere is call equipotential surface

Electric field components parallel to equipotential surface is always zero

**Electric dipole:**

A combination of two charge +q and -q seperated by the distance d

**p**=q

**d**

Where d is the vector joiing negative to positive charge

**Electric potential due to dipole**

V=(1/4πε)(pcosθ/r

^{2})

where r is the distance from the center and θ is angle made by the line from the axis of dipole

**Electric field**

E

_{θ}=(1/4πε)(psinθ/r

^{3})

E

_{r}=(1/4πε)(2pcosθ/r

^{3})

Total E=√E

_{θ}

^{2}+E

_{r}

^{2}

=(p/4πεr

^{3})(√(3cos

^{2}θ+1))

Torque on dipole=

**p**X

**E**

Potential Energy

U=-

**p**.

**E**

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