The electric potential and electric field at any given position
Answers
Answer:
Electric Potential Energy
When you move around in the gravitational field of the earth, you have to make efforts. In other words, you have to work by exerting force if you want to change your position in a field. Electric charges have fields around them and thus a charge has to do work if it intends to change its position. This work is the electric energy or the electric potential energy of the charge.
We know that central forces are conservative in nature. This implies, the work done on any particle moving under its influence does not depend on the path taken by the particle but depends on initial and final positions of the particle. For conservative forces, work done on particle undergoing displacement can be expressed in terms of the potential energy function. Now, we will look at electric potential energy.
How to calculate electric potential energy?
Consider a system of two point charges in which positive test charge q’ moves in the field produced by stationary point charge q shown below in the figure.
Electric Potential Energy
Charge q is fixed at point P and is displaced from point R to S along a radial line PRS shown in the figure. Let r1 be the distance between points P and R and r2 be the distance between P and S. The magnitude of the force on positive test charge as given by Coulomb’s law is:
Electric Potential
If q’ moves towards S through a small displacement dr then work done by this force in making the small displacement dr. Therefore we have: dW=F·dr
Electric Potential
Total work done by this force as test charge moves from point R to S i.e., from r1 to r2 is:
Electric Potential
or
Electric Potential
Thus, for this particular path work done on the test, charge q’ depends on the endpoints and not on the path is taken. Work done W in moving the test charge q’ from point R to S is equal to the change in potential energy in moving the test charge q’ from point R to S. Thus,
W=U(r1)-U(r2) (4)
where
Electric Potential
is the potential energy of test charge q’ when it is at point R and
Electric Potential
is the potential energy of test charge q’ when it is at point S.