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What is the force between two small charges of $2 \times {10^ {- 7}} C$ and $3 \times {10^ {- 7}} C$ placed $30cm$ apart in air?

Last updated date: 13th Jun 2024
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Hint:The Coulomb Act is an experimental law of physics that quantifies the quantity of force between two stationary particles, which are electrically charged. The electrical force between charged bodies at rest is historically referred to as electrostatic or coulomb.

\[F = \dfrac{{{q_1}{q_2}}}{{4\pi {\varepsilon _0} {r^2}}}\]
First charge${q_1} $
Second Charge${q_2} $
Distance between the two charges $r$
${\varepsilon _0} $ is the permittivity of free space

Complete step by step solution:
As an inverse square theorem, the law follows the inverse law of universal gravity of Isaac Newton, except the force of gravity is attractive, while the force of electrostatics can be either attractive or repulsive. The law of Coulomb may be used to derive the law of Gauss and vice versa. For a single stationary point charge, the two laws are identical, describing in separate ways the same physical law.

The magnitude of the electrostatic force of attraction or repulsion between two point loads is directly proportional and inversely proportional to the product of the magnitudes of loads and of the distance between them the power is on the right trajectory that unites them. The electrostatic force is repulsive when the two charges have the same sign; if the signs have opposite signs, the power between them is appealing.

First charge ${q_1} = 2 \times {10^ {- 7}} C$

Second Charge ${q_2} = 3 \times {10^ {- 7}} C$

Distance between the two charges $r = 30cm$

The formula for electrostatic force is given by,

\[F = \dfrac{{{q_1}{q_2}}}{{4\pi {\varepsilon _0} {r^2}}}\]
${\varepsilon _0} $ is the permittivity of free space
$\dfrac {1} {{4\pi {\varepsilon _0}}} = 9 \times {10^9} N {m^2} {C^ {- 2}} $
$F = \dfrac{{2 \times {{10}^{ - 7}} \times 3 \times {{10}^{ - 7}} \times 9 \times {{10}^9}}}{{{{0.3}^2}}}$
$F = 6 \times {10^ {- 3}} N$

Force between the two charges is $6 \times {10^ {- 3}} N$.

Note:The truth of Coulomb’s inverse square rule demands that three requirements be met: The charges must be spherically symmetrical (i.e. point charges or a charged metal sphere). The charges must not overlap (for example, the point fees must be different). The charges ought to be fixed in comparison to each other.