CHARGE consists in product of difference of POTENTIALS at points A and B and value of test charge.             Potential at A                         \[{{V}_{A}}=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{q}{a}\]             Potential at B                         \[{{V}_{B}}=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{q}{a}\]             Thus, work done in carrying a test chargeQ from A to B.                         \[W=({{V}_{A}}-{{V}_{B}})\,(-Q)=0\]

"> CHARGE consists in product of difference of POTENTIALS at points A and B and value of test charge.             Potential at A                         \[{{V}_{A}}=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{q}{a}\]             Potential at B                         \[{{V}_{B}}=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{q}{a}\]             Thus, work done in carrying a test chargeQ from A to B.                         \[W=({{V}_{A}}-{{V}_{B}})\,(-Q)=0\]

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As per this diagram a point charge +q is placed at the origin O. Work done in taking another point chargeQ  from the point A [co-ordinates \[(0,\,\,a)\]] to another points [co-ordinates \[(a,\text{ }0)\]] along the straight path AB is:                  [AIPMT (S) 2005]

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[a] Key Idea: The work done in carrying a test CHARGE consists in product of difference of POTENTIALS at points A and B and value of test charge.             Potential at A                         \[{{V}_{A}}=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{q}{a}\]             Potential at B                         \[{{V}_{B}}=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{q}{a}\]             Thus, work done in carrying a test chargeQ from A to B.                         \[W=({{V}_{A}}-{{V}_{B}})\,(-Q)=0\]

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