why potential at any point in a uniform electric field is not same i.e. why potential difference between any two points in the uniform electric field is not zero?
According to me if i bring a test charge from infinity to a point A in uniform electric
field [assume the field is due to a positive charge] then i will have to apply external force on the test charge against the electrostatic force by the uniform field such that external force is equal to electrostatic force so that kinetic energy of test charge would remain constant thus some potential energy will be stored in the test charge at point A…..NOW if i will bring the test charge from infinity to some another point in the uniform electric field…let the point be B then according to me i will do the same amount of work done on the test charge to bring it to point B because i will apply the external force that will also be equal to electrostatic force by the uniform electric field…..and because the electric field is uniform the test charge will experience the same amount of electrostatic force at each point on the uniform electric field i.e. electrostatic force at both the points A and B due the field will be same.
Hence according to me the potential energy at each point on the uniform electric field will be the same thus the potential also.
Kindly explain…. why not?
thanks!
Electrostatics – Why Electric Potential at Each Point in a Uniform Electric Field Is Not the Same
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Related Solutions
I believe you are confusing the work done by the electric field with the work done on the particle.
By the electric field: The radial force of the electric field is always pointing outwards, and the displacement of the charge in this case is going inward. Thus, the integral you've specified will be negative. That is, the work done by the electric field is negative.
On the Particle: The force that must be applied to the charge (ignoring gravity, relativity, induced vector-potential, etc.) to get it from infinity to the radial distance $r$ is, at the very least, equal and opposite to the force of the electric field acting on the charge. Thus, it is always pointing inwards. Given that the charge is going inwards, the work integral will come out positive.
You can describe the electric force it terms of potential energy, because it is a conservative force. In doing so you actually replace the concept of work done by this force by the concept of potential energy. So you can not longer use both descriptions simultaneously. If you describe the electric force as doing work, then you made positive work and the electric force negative work, so that there is no net gain of kinetic energy in the object. It is a mistake to say that in this description the particle also has potential energy, because in doing so you be considering the work made by the electric field twice (both, as doing work and as gaining potential energy. The descriptions are equivalent, but it is either one or the other. If you chose the potential energy description then you no longer deal with the work of the electric force, as it is implicitly inside the concept of potential energy.
Best Answer
if pt a and b are at equal distance from the charge brought from infinity both points will have the same potential..... as we know dV/dr= E hence it only depends on the distance bw test charge and the other charge.