Electric Potential
Electric potential at a point is the work done per unit positive test charge in bringing it from infinity to that point without changing its kinetic energy.
In one line: Potential has one r in the denominator; field has r squared. Potential is scalar, field is vector.
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- Electric potential tells how much electric potential energy one coulomb of positive charge would have at a point.
- It is a scalar quantity, so only its sign and magnitude matter, not direction.
- For a point charge q, the potential at distance r is V = kq/r, where k = 1/(4 π ε0).
- A positive source charge gives positive potential and a negative source charge gives negative potential when infinity is taken as zero potential.
Example
Formula and rule
V = W/q0, where V is electric potential in volt, W is work done in joule, and q0 is test charge in coulomb.
For a point charge, V = (1/(4 π ε0)) q/r.
Use this when charges are stationary and infinity is the reference point unless another reference is stated.
See it worked out
Follow the example line by line, then use the same method on new questions.
Worked example
A charge of +2 microcoulomb is kept in air.
- 1Find potential at a point 0.30 m away.
- 2V = kq/r = (9.0 × 109)(2.0 × 10−6)/0.30 = 6.0 × 104 V.
- 3The point has positive potential because the source charge is positive.
Method you can reuse
Visual tip
A useful diagram shows a point charge q, a point P at distance r, and infinity as the zero-potential reference. Mark V positive for positive q and negative for negative q.
Check yourself
Answer the question in your head before opening the answer.
Try it yourself
Why is electric potential easier to add than electric field for a system of charges?
Think first, then show answerHide answer
Common wrong answer
Using E = kq/r2 instead of V = kq/r gives the wrong physical quantity and wrong unit.
Don't mix this up
Exam tip
Write it in the exam
Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.
How CBSE asks it
- 1
Enough for 1 mark
Electric potential at a point is the work done per unit positive test charge in bringing it from infinity to that point without changing its kinetic energy.
- 2
Add for 2 marks
Example: Near a positive point charge, a positive test charge has positive potential energy, so the potential is positive. Near an electron, the potential is negative because work is released while bringing a positive test charge from infinity.
- 3
Add for 3 marks
Electric potential tells how much electric potential energy one coulomb of positive charge would have at a point.
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