Question

What is the relationship between electric potential energy charge and potential difference?

Answer 1

this u can understand with an example assume a body in air at x height so it has potential energy similarly electric potential energy at one side whereas potential difference is created when one side is full of electrons than other side.
This both terms interrelated when u talk about one side so it has electric potential energy when talk about two sides with unbalanced amount of electron so there is potential difference created.
Hope it helps!

Answer 2

$\Huge\bf\purple{\mid{\overline{\underline{Answer}}}\mid}$

To derive :-

Relationship between Electric Field and Electric Potential .

Proof:-

First of all , let's consider a charge q located at a specified point and emitting electric field . We shall also consider 2 closely located points named as A and B.

The distance between A and B be dx.

Since the dx distance is extremely small, we can consider that the Electric field E (from the charge) remains same at both the points.

Now the work done to move a unit positive charge from A to B will be :

$\large\dashrightarrow{ \tt{dW = - E \times dx }}$

The negative sign denoted that the work done was against the Electric Field Direction.

For a unit positive charge , we know that work done us equal to the potential difference dV.

$\large\dashrightarrow \: \: \tt{dV = - E \times dx }$

$\large{ \tt{ \dashrightarrow E = - \dfrac{dV}{dx} }}$

So we can say that Electric Field is the gradient of Electric Potential with respect to distance.

$\huge{\mathfrak{\orange{hope\; it\; helps}}}$