Question

1) a) Derive a relationship between the electric field (E) and electric potential (V) knowing that V is defined as the energy per unit test charge.

b) Based on the above derivation, state an alternate acceptable unit for (E).

Answer 1

The work done on the object to move it through infinitesimal displacement    under force   acting on it is given as

_______________________________________relation 1

As per the Work-Energy theorem,

The work done    is equal and opposite to the change in the potential energy .

Using relation 1 in above equation we get,

____________________________________________relation 2

The force   acting on charge    in the electric field    is given as

So, Using above equation in relation 2 we get,

________________________________________relation 3

Since electric potential   is defined as the Energy   per unit charge we have

Taking Gradient on both sides we get,

Using above relation in relation 3 we get,

____________________________________relation 4

  

b)

Let,

Dimension of Electric potential  = ( In SI units )

Dimension of Displacement =   ( In SI units )

Dimension of Electric field

Using Dimensional analysis ( that is dimensions on the left side of the equation must be equal to that on the right side ) on relation 4 we get

,

( In SI units)