**Principle of superposition of electrostatic forces. **

Coulomb’s law gives force between two point charges. The principle of superposition enables us to find the force on a point charge due to a group of point charges. This principle is based on the property that the forces with which two charges attract or repel each other are not affected by the presence of other charges.

The principle of superposition states that when a number of charges are interacting, the total force on a given charge is the **vector sum of the forces exerted on it due to all other charges**. The force between two charges is not affected by the presence of other charges.

Mathematically, the superposition principle can be expressed as follows:

F_{total} = F_{1} + F_{2} + … + F_{n}

where F_{total} is the total force on the charged particle, F_{1}, F_{2}, …, F_{n} are the individual forces exerted on the particle by each of the n other charged particles in the system.

## Numerical Problems Based on Superposition Principle of Electric Forces for Class 12 Physics

Here we are providing numerical problems based on Superposition Principle of Electric Forces for Class 12 Physics.

Q.1.Â Â Ten positively charged particles are kept fixed on the x-axis at points x = 10 cm, 20 cm, 30 cm, …, 100 cm. The first particle has a charge 1.0 Ã— 10^{-8} C, the second 8 Ã— 10^{-8} C, third 27 Ã— 10^{-8} C, and so on. The tenth particle has a charge 1000 Ã— 10^{-8} C. Find the magnitude of the electric force acting on a 1 C charge placed at the origin. (Ans. 4.95 Ã— 10^{5}N)

Q.2. Charges of + 5 Î¼C, + 10 Î¼C and -10 Î¼C are placed in air at the corners A, B and C of an equilateral triangle ABC, having each side equal to 5 cm. Determine the resultant force on the charge at A.

(Ans: 180 N)

Q.3. Charges q_{â†‘} =1.5 mC, q_{2} = 0.2 mC and q_{3} = – 0.5 mC are placed at the points A, B and C respectively, as shown in Fig. If r_{1} = 1.2 m and r_{2 }= 0.6 m, calculate the magnitude of resultant force on q_{2}. (Ans. 3.125 Ã— 10^{3} N)

Q.4. Three point charges +q each are kept at the vertices of an equilateral triangle of side â€˜lâ€™. Determine the magnitude and sign of the charge to be kept at its centroid so that the charges at the vertices remain in equilibrium.

(Ans: -q/**âˆš**3)