Here comes one more concept, and that of Electrostatic Potential. You might recall the gravitational potential.
Gravitational Potential: It is defined as the work done in bringing a unit mass from infinity to that point, against gravitational force without acceleration. Keep in mind it is defined at a point.
Electrostatics potential: It is defined as the work done in bringing unit positive charge from infinity to that point against electrostatic force without acceleration. Again it is defined at a point.
This is basically definition of absolute potential. But this does not carry physical significance. WHO will go to infinity ? Then how is concept of potential useful to us ?
Let us analyse. Hypothetically to bring a charge from infinity to a point A we do work W1 and to reach point B we do work W2. So W1 and W2 might be hypothetical but W1 – W2 definitely gives the amount of work done in transferring charge from A to B and that is relevant. So we can say that potential difference is basically or concern. By convention we take potential of earth to be zero. As we progress you will be understanding it better !
So practically W = qDV, where q is the charge moved and DV is the potential difference between points, then W is the work done.
The derivations can be downloaded here. Also in Video from link.
Now it is also to be understood that in electrostatics we can find work by using W = F.x and also W = qDV, any difference? Not actually but in W = F.x unless F is constant we cannot simply multiply, for variable force we have to integrate it. But in potential method it is simpler, because potential is a state function. It doesn’t depend on the path followed but only initial and final position.
Mathematically the potential at distance ‘r’ from charge ‘q’ is given as kq/r.
Relation between electric field E and potential : when charge ‘q’ is brought near ‘Q’ from infinity via route AB, we study work by potential and also by force due to E and equate them to get relation.
When charge Q is placed and ‘q’ is kept at A the force between is F = qE where E is the electric field due to charge ‘Q’. work done by agent to bring charge nearer ‘dr’ will do work
dW = qE.dr = -qE dr (-ve as force & displacement are opposite direction) also dW = q dV (work done across potential dV in moving charge ‘q’ using formula W = qV)
Equating these we get very important relation E = -dV/dr or it can be stated that electric field is also equal to negative of potential gradient. Here also we get new unit of electrical field as Volt/meter. Previously we had Newton/Coulomb. Both are equivalent
With this relation between the electric field and potential, we must understand one more consequence of it. Whenever we get E as zero the potential has to be constant, but not necessarily zero. Now in any conductor the electrical field in electrostatics is zero. So the potential inside conductor is same as that at surface. You will see this in numericals video in details as well.
Now we discuss about the concept of potential energy! Recall the basic of potential energy of any system is amount of work done in creating the system. We will use the same concept here.
If a point near a charge Q has potential V (V = kQ/r) that simply means the amount of work done in bringing 1 coulomb charge is V, to bring 2 coulomb it will be 2V and similarly for q charge it will be qV and hence kQq/r. Where ‘r’ is the distance between the charges.
Do remember that in this case of potential and potential energy also the principle of superposition is applied. But as these quantities are scalar we will have to use scalar addition in this case, unlike electric field where we used vector addition.
DO THESE NUMERICALS
THEN if required go to solutions in video
Lastly we conclude with the concept of equipotential surface, it is defined as the surface where the potential is same and NO work is done in this case on moving charges. You may see from the examples in the images as well.