I recently read that electric potential at a point is defined as work done in bringing a positive unit charge from infinity (or any other reference point) to that point. How can electric potential be equal to work done? Won't they dimensionally be different? What am I missing out here? If this is not correct please share an intuitive explanation and the exact definition.
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2$\begingroup$ Just divide by the charge of the positive unit charge; and by definition of "unit", that means it is one. Then the units will work out. $\endgroup$– naturallyInconsistentCommented May 31 at 10:04
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$\begingroup$ It is the work done per charge. Then the units match. $\endgroup$– SteevenCommented May 31 at 12:29
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3 Answers
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Indeed, electric potential and work have different units.
This is implied by the phrase "work per unit charge", which implies that we are taking the work $W$ and dividing it by the charge involved, $q$, so that the resulting quantity, $V=W/q$, has units of work divided by charge.
This is the same as when we say things like "density is mass per unit volume", i.e. $\rho=m/V$, where the implication is that density has units of mass divided by volume.
answered May 31 at 10:48
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It equals the work done per unit charge.
From an operational point of view:
- the work done on a test charge linearly depends on the charge;
- characteristics of the field are independent from the test charge;
- thus, the potential is defined as the ratio of the work done and the charge, like the electric field is defined as the ratio of the force acting on the charge and the charge itself.
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It is simple . We already know that work done is energy.Potential is also a form of energy .So electic potential is equal work done per unit charge
