Question

Calculate the magnitude of the electric potential difference across the length

Answer 1

Batteries and Potential Difference.

A battery is a device that stores positive charge on one of its terminals and negative charge on the other terminal.

Electric Potential Energy.

Potential energy can be defined as the capacity for doing work which arises from position.

In the electrical case, a charge will exert a force on any other charge and potential energy arises from any collection of charges.

For example, if a positive charge Q₁ is fixed at some point in space, any other positive charge which is brought close to it will experience a repulsive force and will therefore have potential energy. The potential energy of a test charge Q₂ in the vicinity of this source charge will be:

Electric Potential.

At a point in space, the electric potential is the potential energy per unit of charge that is associated with a static electric field. It is a scalar quantity, typically measured in volts.

Potential at a point is defined as the work done in moving a charge of 1 coulomb from infinity to that point. Symbol for potential at the point A is

V_A

The difference in electrical potential between two points is known as the potential difference or voltage.

Potential Difference between two charged metal plates A and B

              A       B

              +        -

The electric field that exists between two metal plates is uniform except at the edges. Check the diagrams for the electric field lines.

If an electron ( -ve charge ) were moved from the positive plate A to the negative plate B, work would have to be done to overcome the force of repulsion between the -ve electron and the -vely charge metal plate at B.

This work would be stored in the election as potential energy as long as the election remains at plate B. This is also true if a +ve charge is moved from plate B to A.

Because of this change in potential energy we say that there is a difference in potential or potential difference ( p.d. ) between the plates.

The potential difference in this context is an indication of the amount of work that would be done in moving a charge between two points.

The S.I. unit of potential difference is called the Volt and the potential difference is also called voltage.

The unit Volt is defined as follows : There is a potential difference of 1 Volt between two points when 1 Joule of work has to be done to move 1 Coulomb of charge between the two points.

V_{A B} is symbol for the potential difference between A and B

Note also V_AB   =    V_A - V_B

Relationship between potential difference V and work done (energy) is given by

              WORK DONE = Q . V.

Relationship between Electric Field Intensity ( E ) and Potential V at a distance of r(m) from a point charge is given by

                    

Relationship between Electric Field Intensity ( E ) and Potential difference V between two parallel charge metal plates a distance d (m) apart is given by

Also it is important to note that Potential or Potential difference is a scalar quantity and this is always the case the

if Q is -ve then the potential is negative    and

if Q is +ve then the potential is positive.

Electric Dipole: Equal and opposite point charges a distance r (m) apart.

              Q₁                       Q₂

                                      r (m)

Example 1.An electric dipole has a positive charge of 20mC and a length of 0.5mm.

Calculate (i)   the electric force between the two charges  

(ii) Electric field intensity at the midpoint (A) of the dipole.

(iii) The potential at the midpoint.

              Q₁          A           Q₂

                                      r (m)