If the three similar charges of magnitude +q are placed on the vertices of an equilateral triangle of side a, then find the \(\frac{F_{12}}{F_{23}}\)

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Airforce Group X 12 Jul 2021 Shift 1 Memory Based Paper

Option 2 : 1 : 1

__CONCEPT:__

The force between multiple charges:

- Experimentally, it is verified that force on any charge due to a number of other charges is the vector sum of all the forces on that charge due to the other charges, taken one at a time.
- The individual forces are unaffected due to the presence of other charges. This is termed as the principle of superposition.
- The principle of superposition says that in a system of charges q1, q2, q3,..., qn, the force on q1 due to q2 is the same as given by Coulomb’s law, i.e., it is unaffected by the presence of the other charges q2, q3,..., qn. The total force F1 on the charge q1, due to all other charges, is then given by the vector sum of the forces F12, F13, ..., F1n.

⇒ \(\vec{F_1}=\vec{F_{12}}+\vec{F_{13}}+...+\vec{F_{1n}}\)

__CALCULATION__:

Given: q_{1} = q_{2} = q_{3} = q (let)

F12 = Force on charged particle A due to charge particle B

F23 = Force on charged particle B due to charge particle C

F31 = Force on charged particle C due to charged particle A

- Force on charged particle A due to charge particle B is

⇒ \({F_{12}} = \frac{Kq_1q_2}{a^2}=\frac{Kq^2}{a^2}\) ------(1)

Force on charged particle B due to charge particle C is

⇒ \( {F_{23}} = \frac{Kq_2q_3}{a^2}=\frac{Kq^2}{a^2}\) ------(2)

On dividing equations 1 and 2, we get

⇒ \( \frac{F_{12}}{F_{23}}=\frac{\frac{Kq^2}{a^2}}{\frac{Kq^2}{a^2}}=\frac{1}{1}\)