Question

Force between two charges separated by a certain distance in air is F. If each charge is doubled and the distance between them is also doubled,force would be

Answer 1

Answer:

Coulomb’s law, mathematical description of the electric force between charged objects. Formulated by the 18th-century French physicist Charles-Augustin de Coulomb, it is analogous to Isaac Newton’s law of gravity.

Figure 1: Electric force between two charges (see text).

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electricity: Coulomb’s law

Static electricity is a familiar electric phenomenon in which charged particles are transferred from one body to another. For example, if…

Both gravitational and electric forces decrease with the square of the distance between the objects, and both forces act along a line between them. In Coulomb’s law, however, the magnitude and sign of the electric force are determined by the electric charge, rather than the mass, of an object. Thus, charge determines how electromagnetism influences the motion of charged objects. Charge is a basic property of matter. Every constituent of matter has an electric charge with a value that can be positive, negative, or zero. For example, electrons are negatively charged, and atomic nuclei are positively charged. Most bulk matter has an equal amount of positive and negative charge and thus has zero net charge.

According to Coulomb, the electric force for charges at rest has the following properties:

   Like charges repel each other; unlike charges attract. Thus, two negative charges repel one another, while a positive charge attracts a negative charge.

   The attraction or repulsion acts along the line between the two charges.

   The size of the force varies inversely as the square of the distance between the two charges. Therefore, if the distance between the two charges is doubled, the attraction or repulsion becomes weaker, decreasing to one-fourth of the original value. If the charges come 10 times closer, the size of the force increases by a factor of 100.

   The size of the force is proportional to the value of each charge. The unit used to measure charge is the coulomb (C). If there were two positive charges, one of 0.1 coulomb and the second of 0.2 coulomb, they would repel each other with a force that depends on the product 0.2 × 0.1. Thus, if each of the charges were reduced by one-half, the repulsion would be reduced to one-quarter of its former value.#BAL

Explanation:

Answer 2

Force between two charges after each charge is doubled and the distance is also doubled remains unchanged.

• COULOMB'S INVERSE SQUARE LAW: The electrostatic force of interaction(attraction or repulsion) between two point charges is directly proportional to the scalar  of the magnitudes of charges and inversely proportional to the square of the distance between them.

                             F ∝ $\frac{q_{1}q_{2} }{r^{2} }$

                             F = k$\frac{q_{1}q_{2} }{r^{2} }$

• Here, $q_{1}, q_{2}$ are charges and r is the distance between them.

PROBLEM:

                            $F_{1} = k\frac{q_{1}q_{2} }{r^{2} }$ ------------------(1)

Given that charges and distance is doubled

                          $q_{1}$' = $2q_{1}$   $q_{2}$' = $2q_{2}$   r' = 2r

                            $F_{2}$ = k$\frac{2q_{1}2q_{2} }{(2r)^{2} }$

                            $F_{2}$ = k$\frac{4q_{1}q_{2} }{4r^{2} }$

                            $F_{2}$ = k$\frac{q_{1}q_{2} }{r^{2} }$ --------------------(2)

From (1) and (2), we get

                              $F_{1} = F_{2}$

Therefore, force does not change even if the charges and the distance between them is changed.