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Derive an expression for the electric po...

Derive an expression for the electric potential due to a point charge.

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Expression for the electric potential due to a point charge.
1. Electric potential at a point is defined as the amount of workdone in moving a nuit `+ve` charge from infinity to that point.

2. Consider a point P at a distance r from the point charge having charge `+q`. The electric field at `P=E=(q)/(4piepsi_0x^2)` .
3. Workdone in taking a unit `+ve` charge from B to `A=d V=-E`. dx(-ve sign shown that the workdone is `+ve` in the direction B to A. Whereas the potential difference is `+ve` in the direction A to B .
4. Therefore , potential at `P=` The amount of workdone in taking a unit `+ve` charge from infinity to P
`V=-int_(oo)^(r)E-dx=-(1)/(4piepsi_0)int_(oo)^(r)(q)/(x^2)dx`
`=(1)/(4piepsi_0)[(q)/(x)]_(oo)^(r)=(1)/(4piepsi_0)((q)/(r)-(q)/(oo))=(1)/(4piepsi_0)(q)/(r)`
`therefore V=(1)/(4piepsi_0)(q)/(r)`.
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