Coulomb’s law Problems and Applications

Coulomb’s Law

Coulomb’s law enables us to calculate the electrostatic force between any two point charges. It holds for distances ranging from 10-15 to 1018 m.

The force of interaction between any two point charges is directly proportional to the product of the electrical charges and inversely proportional to the square of the distance between them.

  • If the charges are of same sign – force is repulsive.
  • If the charges are of opposite sign – force is attractive.

\[F_{e}=\frac{K q_{1}q_{2}}{r^{2}}\]

Unite used  $q_{1},q_{2}$ are in coulomb, $F$ in newton and $r$ in metres.

$\epsilon_{o}$ is permittivity of free space,

\[\epsilon_{o}=8.854 \times 10^{-12}C^{2}/N-m^{2}\]

Dimesnsional formul of $\epsilon_{o}$ is [M-1L-3T4A2].

$K $ is a constant, its standard unit is,

\[K=\frac{1}{4 \pi \epsilon_{o}r^{2}} \simeq 9 \times 10^{9}N-m^{2}/C^{2} \]

Important points of Coulomb’s law

  • The coulomb’s law obey Newton’s third law,

\[F_{12}= -F_{21}\]

i.e. The two charges exert equal and opposite forces on each other.

  • The electrical forces are conservative in nature.
  • When the dielectric medium is completely filled in between charges, then the force between them decreases by a factor of dielectric constant$K$.

\[F_{\text{dielectric filled}}=\frac{F_{\text{without dielectric}}}{Kr}\times \frac{q_{1}q_{2}}{r^{2}}\]

as $\epsilon = \epsilon_{o}K$ is called permittivity of the medium,

\[F_{\text{dielectric filled}}= \frac{1}{4 \pi \epsilon} \times \frac{q_{1}q_{2}}{r^{2}}\]

  • Electric force is much stronge than gravitational force.

\[F_{e}=\frac{K q_{1}q_{2}}{r^{2}}\]

and

\[F_{g}=\frac{G m_{1}m_{2}}{r^{2}}\]

as,

\[K=\simeq 9 \times 10^{9}N-m^{2}/C^{2} \]

\[G=6.67 \times 10^{-11}N-m^{2}kg^{-2}\]

Thus, $F_{e} >>F_{g}$

Application of Coulomb’s Law

  1. Solving problem related to string.
  2. Lami’s Theorem

Similarity between Electrostatic and Gravitational forces

  • Electrostatic and Gravitational forces obey the inverse square law.
  • Both are central forces.
  • Both are conservative forces.

Difference between Electrostatic and Gravitational forces

  • Electrostatic forces are between two charges and gravitational forces are between two masses.
  • Gravitational forces are always attractive but electrostatic forces may be attractive or repulsive.
  • Electrostatic forces are 1036 times stronger than gravitational forces.
  • Electrostatic force operates over short distances while gravitational forces operate over very large distances.