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Define electric potential due to a pointcharge and arrive at the expression for the electric potentialat a point due to a point charge. |
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Answer» <P> Solution :The electric potentialat a pointdue to a givenpoint charge may be measured by finding the AMOUNT of work required to bringa unit positivetest charge , from a pointat infinityto that POINT inside a fieldregion.Let .P. be a point at infinity . Let A,B and C be points inside the field . Let BC =dx. Let the displacementbe .dx.and .+1C. is broughtcloserby .dx.in a directionopposite to the directionof electric field . Amountwork DONE =-Fdx For .+1C.of charges , F=E and dW=dV where .dV.is electric potentialdefinedas `dV=(dW)/(q_0)` where `q_0=+1C` of testcharge. Electric field intensity at`C=(1/(4piepsilon_0))(q/x^2)` .  Hence , dV=-Edx. Electric potentialat .A. `V_A=int_oo^r dV=-int_oo^r (1/(4piepsilon_0))(q/x^2)dx` i.e., `V_A=-(1/(4piepsilon_0))q((-1)/x)_oo^r` i.e.,`V_A=(1/(4piepsilon_0))q[1/r-1/oo]` i.e., `V_A=(1/(4piepsilon_0))(q/r)` Hence, electric potentialat a point is inverselyproportionalto the distanceof thatpoint . |
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