Electrostatics - Long Question Answer | Physics Grade 11 Solution

Long Question Solution

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Electrostatics - Long Question Answer | Physics Grade 11 Solution

Electrostatics - Long Question Answer 3

Question: Define electric potential and derive an expression for it due to a point charge at a distance ‘d’ from it.
The electric potential at a point inside the electric field is defined as the amount of work done in moving a unit positive charge (test charge) from infinity to that point.
If WꚙA is the amount of work done in moving unit positive charge from infinity to point A, then, it is equal to the electric potential at that point A.
i.e. V = WꚙA

Electric potential

Suppose a unit positive charge is at any point P at a distance x and point charge +q situated at O so that OP = x.
Since the force experienced by unit positive charge is equal to the electric intensity at that point, we have
     F = 1/4πϵ0  (q/x2)
The work done in moving a unit positive charge from P to Q through small distance dx is.
    dW = F * (-dx) = -1/4πϵ0 (q/ x2) dx
where -ve sign indicates work is done against electrostatic force.
Therefore, the total work done in moving a unit positive charge from infinity to point A is,
   WꚙA = ∫dW
          = - ∫r  (q/4πϵ0r2) dx
          = 1/ 4πϵ0 (q/r)
Therefore, the electric potential at point A is V = 1/ 4πϵ0 (q/r)

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