Define electric potential due to a point charge and arrive at the expression for the electric potential at a point due to a point charge in its vicinity.
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The electrostatic potential at any point in an electrostatic field is defined as the work done in carrying a unit positive charge from infinity to that point against the electrostatic force of the field.
Consider a point Charge +Q at O. Let P be a point at a distance r from O. Consider a point A at a distance x from O. The magnitude of electrostatic force on unit-positive charge at A, is F=4πε01x2Q×i F=4πε0x2Q along OP Work Done in moving a unit positive charge from A to B through a small distance dx is, ΔW=F.dx=Fdxcos180o ΔW=−Fdx ΔW=4πε0x2−Qdx Total work done in moving a unit positive change from infinity to the point P is, W=∫∞r4πε0−1x2Qdx=−4πε0x2Q∫∞rx21dx
W=4πε0rQ By definition, this work done is equal to the electrostatic potential (V) at that point due to Q. V=4πε01rQ
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