What is the relationship between electric potential and work done?

[ojsimon]

Hi

I am sure this is very basic but i am struggling to derive or work this out, and i have looked, on the internet and textbooks and can't find this.

The electric potential at a point is defined as the work done per unit charge to move a small test charge from infinity to that point.

And an equation for it is : EP = k*(Q/R)

I want to get back to the definition from this equation, but i can't get very far:

here is what i have done: WD= work done

Q/R = (wd/v)/R
= wd/vR


But i can't go much further without it just going back to the original form... Can anyone help me?

Thanks

 

[tiny-tim]

hi ojsimon!

(what's v ? )

work done = ∫ force d(distance) = ∫_∞^R kQ/r² dr

(and d(work done)/dr = force)

 

[ojsimon]

sorry v was meant to be voltage and came from the equation v=wd/q

Thanks although i don't quite understand your integral?

Thanks

 

[tiny-tim]

Thanks although i don't quite understand your integral?

The integral is the force integrated from infinity to the distance R, since the PE is the work done to get the charge from infinity to R.

 

[sardar]

for your question. The relationship between electric potential and work done is a fundamental concept in the field of electromagnetism. Essentially, electric potential is a measure of the potential energy that a charged particle possesses at a particular point in an electric field. This potential energy is due to the work done on the particle by the electric field.

To understand this relationship better, let's break down the equation you provided: EP = k*(Q/R). Here, EP represents the electric potential, k is a constant (usually Coulomb's constant), Q is the charge of the particle, and R is the distance from the particle to the source of the electric field.

As you correctly stated, the electric potential is defined as the work done per unit charge (WD/Q) to move a small test charge from infinity to that point. This can also be written as WD = EP * Q. Plugging this into the equation above, we get:

EP * Q = k * (Q/R)

Solving for EP, we get:

EP = k * (Q/R) * (1/Q)

Simplifying, we get:

EP = k/R

This shows that the electric potential is directly proportional to the strength of the electric field, which is represented by k, and inversely proportional to the distance from the particle to the source of the electric field, represented by R.

In terms of work done, the equation shows that the work done (WD) is equal to the electric potential (EP) multiplied by the charge (Q). This means that the greater the electric potential, the more work is done on the particle, and vice versa.

I hope this explanation helps you understand the relationship between electric potential and work done better. If you have any further questions, please don't hesitate to ask.