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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.

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Student-friendly explanation

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 pi epsilon0). A positive source charge gives positive potential and a negative source charge gives negative potential when infinity is taken as zero potential.

How to write this in exams

  1. 1

    Start with the exact idea

    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. 2

    Then show how to use it

    Identify the source charge; write V = kq/r; convert microcoulomb or nanocoulomb to coulomb; substitute distance in metre; keep the sign of charge; add scalar potentials if more than one charge is present.

  3. 3

    Add one concrete 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.

  4. 4

    Avoid this incomplete answer

    Using E = kq/r^2 instead of V = kq/r gives the wrong physical quantity and wrong unit.

Definition

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.

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.

Rule to remember

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 pi epsilon0)) q/r. Use this when charges are stationary and infinity is the reference point unless another reference is stated.

Memory hook

Potential has one r in the denominator; field has r squared. Potential is scalar, field is vector.

Examples and method

Worked example

A charge of +2 microcoulomb is kept in air. Find potential at a point 0.30 m away. V = kq/r = (9.0 x 10^9)(2.0 x 10^-6)/0.30 = 6.0 x 10^4 V. The point has positive potential because the source charge is positive.

Method to apply

Identify the source charge; write V = kq/r; convert microcoulomb or nanocoulomb to coulomb; substitute distance in metre; keep the sign of charge; add scalar potentials if more than one charge is present.

Diagram support

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.

How CBSE asks it

Questions usually ask for definition, SI unit, scalar nature, potential due to a point charge, or net potential due to two or more charges.

Avoid common mistakes

Common confusion

Students often treat electric potential as a vector like electric field. Potential is scalar, so potentials are added with signs, not by components.

Common wrong answer

Using E = kq/r^2 instead of V = kq/r gives the wrong physical quantity and wrong unit.

Exam tip

In numericals, first decide the sign of each source charge, then substitute in V = kq/r. Do not put the test charge into the formula for potential due to a source charge.

Quick check

Why is electric potential easier to add than electric field for a system of charges?

Electric potential is easier to add because it is a scalar quantity. The net potential is the algebraic sum of kq/r terms, including the signs of charges, while electric field needs vector addition with directions.

Answer writing and exam use

1-mark answer

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-mark answer

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. 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 pi epsilon0)) q/r. Use this when charges are stationary and infinity is the reference point unless another reference is stated. 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-mark answer

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 pi epsilon0). A positive source charge gives positive potential and a negative source charge gives negative potential when infinity is taken as zero potential. 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 pi epsilon0)) q/r. Use this when charges are stationary and infinity is the reference point unless another reference is stated. A charge of +2 microcoulomb is kept in air. Find potential at a point 0.30 m away. V = kq/r = (9.0 x 10^9)(2.0 x 10^-6)/0.30 = 6.0 x 10^4 V. The point has positive potential because the source charge is positive. Questions usually ask for definition, SI unit, scalar nature, potential due to a point charge, or net potential due to two or more charges. Using E = kq/r^2 instead of V = kq/r gives the wrong physical quantity and wrong unit.
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