Iwo small charged spheres repel each other with a force 2 ×10^-3 N. The charge on one sphere is

step 1 Hi friends here it is given for separation between the two charges to be a separation between Q1

Iwo small charged spheres repel each other with a force 2...

Iwo small charged spheres repel each other with a force $2 \times 10^{-3} \mathrm{~N}$. The charge on one sphere is twice that of the other. When these two spheres displaced $10 \mathrm{~cm}$ further apart the force is $5 \times 10^{-4} \mathrm{~N}$, then the charges on both the spheres are....... (A) $1.6 \times 10^{-9} \mathrm{C}, 3.2 \times 10^{-9} \mathrm{C}$ (B) $3.4 \times 10^{-9} \mathrm{C}, 11.56 \times 10^{-9} \mathrm{C}$ (C) $33.33 \times 10^{9} \mathrm{C}, 66.66 \times 10^{-9} \mathrm{C}$ (D) $2.1 \times 10^{-9} \mathrm{C}, 4.41 \times 10^{-9} \mathrm{C}$

Iwo small charged spheres repel each other with a force $2 \times 10^{-3} \mathrm{~N}$. The charge on one sphere is twice that of the other. When these two spheres displaced $10 \mathrm{~cm}$ further apart the force is $5 \times 10^{-4} \mathrm{~N}$, then the charges on both the spheres are.......
(A) $1.6 \times 10^{-9} \mathrm{C}, 3.2 \times 10^{-9} \mathrm{C}$
(B) $3.4 \times 10^{-9} \mathrm{C}, 11.56 \times 10^{-9} \mathrm{C}$
(C) $33.33 \times 10^{9} \mathrm{C}, 66.66 \times 10^{-9} \mathrm{C}$
(D) $2.1 \times 10^{-9} \mathrm{C}, 4.41 \times 10^{-9} \mathrm{C}$

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Key Concepts

Coulomb's Law

This fundamental law of electrostatics quantifies the force between two point charges. It states that the magnitude of the electrostatic force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. This law is essential for calculating forces in systems involving charged particles.

Inverse Square Law

The inverse square law is a core principle in physics that describes how certain physical quantities (like the electrostatic force in this case) diminish with the square of the distance from the source. When the distance between two charges increases, the force decreases by the square of that change, which is crucial for understanding the relationship between force and distance in electrostatic interactions.

Charge Proportionality and Scaling

In problems where charges are compared or scaled relative to one another, proportional reasoning is used to relate the magnitudes of different charges. When one charge is described as being a multiple of the other, the force calculations based on Coulomb’s law must incorporate this ratio, which can be pivotal in determining the individual charge values given the net force and distance information.

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