Relation Between Electric Field And Potential - Practice Questions & MCQ

Electric field and potential are related as

Where E is Electric field

And V is Electric potential

And r is the position vector 

And Negative sign indicates that in the direction of intensity the potential decreases.

Then 

where

  (partial derivative of V w.r.t. x)

    (partial derivative of V w.r.t. y)

    (partial derivative of V w.r.t. z)

Proof-

Let the Electric field at a point r due to a given mass distribution is E.

If a test charge q is placed inside a uniform Electric field E.

Then force on a charged particle q when it is at r is   as shown in figure

As the particle is displaced from r to r + dr the

work done by the Electric force on it is

Electric potential V is defined as the negative of work done by electric force per unit charge

So  Integrating between r₁, and r₂

We get 

If r₁=r₀, is taken at the reference point, V(r₀) = 0. 

Then the potential V(r₂=r) at any point r is 

in Cartesian coordinates, we can write

Then 

So  

If y and z remain constant, dy = dz = 0

Thus 

Similarly  

• When an electric field is a uniform (constant)

As Electric field and potential are related as 

and E=constant then  

• If at any region E = 0 then V = constant
• If V = 0 then E may or may not be zero.