ELECTRIC POTENTIAL

SLIDES BY ZIL E HUMA

ELECTRIC POTENTIAL

The force between two charges depends on the magnitude and sign of each charge.

DEF: The potential energy per unit test

charge is known as the electric potential.

Let we have a collection of charges . We have to determine the electric

potential of these charges at a point P. We place a +ve test charge at the infinite

distance from the collection of charges, where the electric potential will be zero.

We then move this test charge from infinity to the point P, and in this process the potential energy changes from 0 (zero)

to Up.

The electric potential Vp at P due to the collection of charges is then defined as

Vp = Up/qo

where the qo is the test charge. Electric potential is a scalar

quantity because Up and qo both are the

scalar quantities.

The potential is independent of the size of the test charge.

qo is a very small charge so it has the negligible effect on the group of charges.

Depending on the distribution of charges, the potential Vp may be +ve, -ve or zero.

According to the above equation the potential energy is positive.

If we move the positive test charge from infinity to that point, the electric field do negative work, which indicates that the test charge has experienced a repulsive force.

ELECTRIC POTENTIAL BETWEEN TWO POINTS a AND b.

We move a test charge qo from a to b. The electric potential difference is

defined by V = Vb - Va = (Ua – Ub) / qo

The potential at b may be greater than, less than, or the same as the potential at a,depending on the difference between the two points .

UNIT OF THE ELECTRIC POTENTIAL

The SI unit of potential that follow the above equation is the

joule / coulomb which is equal to the volt (abbreviated

V) .

1 volt = 1 joule / coulomb

So we have U = q V

When any charge q moves between two points whose potential difference is V, the system experiences a change in potential energy U.

When V is expressed in volts and q in coulombs, U comes out in joules.

ELECTRON VOLT

Electron volt is the unit of energy. If we express V in volts and q in units

of the elementary charge e, then U is expressed electron volt (eV).

POTENTIAL DUE TO A POINT CHARGE

+ + aq

b

rb

ra

ds

qoE

A test charge qo moves from a to b along a radial line from a positive charge q that establishes an electric field E.

These two points a and b are near an isolated positive point charge q.

A positive charge qo moves from point a to b along a radial line. From figure we can see that both E and ds has the radial component i.e.,dr

So ds = dr E.dr =E dr We know already that

Vb – Va = - E.ds = - E.dr = - E dr

Using the expression for the electric field of a point charge,

E = q/4 0 r²

So we have

Vb – Va = -q/40 dr/r²

integration limits are between ra and rb .

= q/40 (1/rb – 1/ra )This equation gives the potential difference

between the points a and b.

.

If we wish to find the potential difference at any point , then we choose a reference point at infinity. We choose a to be at infinity and define Va to be zero at this position.

Making these substitutions and dropping the subscript b we get

V = 1/40 (q / r) This equation is also valid for any spherically

symmetric distribution of total charge q,as long as r is greater than the radius of the distribution.

POTENTIAL DUE TO A COLLECTION OF POINT CHARGES

The potential at any point due to a group of N charges is found by

1.Calculating the potential Vi due to each charge, as if the other charges were not present, and

2. Adding the quantities so obtained. V = V1 + V2 + V3 + ………..+ VN

So we have i=N

V = Vi = 1/40qi/ri

i=1 i

where qi is the value (magnitude and sign) of the ith charge.

And ri is the distance of the ith charge from the point in question.