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Coulomb's Law and Force Between Point Charges

Coulomb's law states that the electrostatic force between two stationary point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them, acting along the line joining the charges.

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Student-friendly explanation

For two point charges q1 and q2 separated by distance r in vacuum, the magnitude of force is F = (1/4πε0)(|q1q2|/r^2). The constant 1/4πε0 is approximately 9 x 10^9 N m^2 C^-2. Like charges repel and unlike charges attract. The force on each charge has equal magnitude and opposite direction. Coulomb's law is valid for point charges or spherically symmetric charge distributions when separation is measured between centres.

How to write this in exams

  1. 1

    Start with the exact idea

    Coulomb's law states that the electrostatic force between two stationary point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them, acting along the line joining the charges.

  2. 2

    Then show how to use it

    Convert all quantities to SI units. Write Coulomb's formula. Substitute magnitudes of charges and distance. Calculate force. Use charge signs to state attraction or repulsion and draw direction if required.

  3. 3

    Add one concrete example

    Two charges +2 microC and +3 microC separated by 0.30 m repel each other with force F = 9 x 10^9 x (2 x 10^-6)(3 x 10^-6)/(0.30)^2 = 0.6 N.

  4. 4

    Avoid this incomplete answer

    For q1 = +4 microC and q2 = -2 microC, answering -1.8 N as force magnitude is wrong. Magnitude is positive; the negative sign is represented through direction or attraction.

Definition

Coulomb's law states that the electrostatic force between two stationary point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them, acting along the line joining the charges.

Example

Two charges +2 microC and +3 microC separated by 0.30 m repel each other with force F = 9 x 10^9 x (2 x 10^-6)(3 x 10^-6)/(0.30)^2 = 0.6 N.

Rule to remember

F = (1/4πε0)(q1q2/r^2) in vector form with direction along the line joining the charges. F is in newton, q1 and q2 in coulomb, r in metre, and 1/4πε0 = 9 x 10^9 N m^2 C^-2. Use only for stationary point charges in electrostatics or equivalent spherical charge distributions.

Memory hook

Product of charges on top, square of distance below; signs tell direction, not the size of magnitude.

Examples and method

Worked example

Charges q1 = +4 microC and q2 = -2 microC are 20 cm apart. Convert: q1 = 4 x 10^-6 C, q2 = 2 x 10^-6 C, r = 0.20 m. F = 9 x 10^9 x (4 x 10^-6)(2 x 10^-6)/(0.20)^2 = 1.8 N. Since charges are unlike, the force is attractive.

Method to apply

Convert all quantities to SI units. Write Coulomb's formula. Substitute magnitudes of charges and distance. Calculate force. Use charge signs to state attraction or repulsion and draw direction if required.

Diagram support

Required diagram: two point charges q1 and q2 separated by distance r, line joining them, force on q1 and force on q2 shown in opposite directions. For unlike charges arrows point toward each other; for like charges arrows point away from each other.

How CBSE asks it

Asked as a statement with formula and units, a direct numerical, a comparison when distance changes, or a vector-direction question involving two or more charges.

Avoid common mistakes

Common confusion

A frequent mistake is substituting distance in centimetres instead of metres, or using q1 + q2 instead of q1q2.

Common wrong answer

For q1 = +4 microC and q2 = -2 microC, answering -1.8 N as force magnitude is wrong. Magnitude is positive; the negative sign is represented through direction or attraction.

Exam tip

For numerical questions, first convert microC to C and cm to m. Use signs to decide attraction or repulsion, but use magnitudes for force magnitude.

Quick check

If the distance between two point charges is doubled, what happens to the electrostatic force?

The force becomes one-fourth of its original value because Coulomb's force varies inversely as r^2. When r becomes 2r, the denominator becomes 4r^2.

Answer writing and exam use

1-mark answer

Coulomb's law states that the electrostatic force between two stationary point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them, acting along the line joining the charges.

2-mark answer

Coulomb's law states that the electrostatic force between two stationary point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them, acting along the line joining the charges. F = (1/4πε0)(q1q2/r^2) in vector form with direction along the line joining the charges. F is in newton, q1 and q2 in coulomb, r in metre, and 1/4πε0 = 9 x 10^9 N m^2 C^-2. Use only for stationary point charges in electrostatics or equivalent spherical charge distributions. Two charges +2 microC and +3 microC separated by 0.30 m repel each other with force F = 9 x 10^9 x (2 x 10^-6)(3 x 10^-6)/(0.30)^2 = 0.6 N.

3-mark answer

For two point charges q1 and q2 separated by distance r in vacuum, the magnitude of force is F = (1/4πε0)(|q1q2|/r^2). The constant 1/4πε0 is approximately 9 x 10^9 N m^2 C^-2. Like charges repel and unlike charges attract. The force on each charge has equal magnitude and opposite direction. Coulomb's law is valid for point charges or spherically symmetric charge distributions when separation is measured between centres. F = (1/4πε0)(q1q2/r^2) in vector form with direction along the line joining the charges. F is in newton, q1 and q2 in coulomb, r in metre, and 1/4πε0 = 9 x 10^9 N m^2 C^-2. Use only for stationary point charges in electrostatics or equivalent spherical charge distributions. Charges q1 = +4 microC and q2 = -2 microC are 20 cm apart. Convert: q1 = 4 x 10^-6 C, q2 = 2 x 10^-6 C, r = 0.20 m. F = 9 x 10^9 x (4 x 10^-6)(2 x 10^-6)/(0.20)^2 = 1.8 N. Since charges are unlike, the force is attractive. Asked as a statement with formula and units, a direct numerical, a comparison when distance changes, or a vector-direction question involving two or more charges. For q1 = +4 microC and q2 = -2 microC, answering -1.8 N as force magnitude is wrong. Magnitude is positive; the negative sign is represented through direction or attraction.
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