Question

Three equal charges are placed on the three corner of a square. If the force between q1 and q2 is F12 and that between q1 and q3 is F13, the ratio of the magnitude F12/F13 is

Answer 1

Answer:

Concept:

Always pointing away from a positive charge and in the direction of a negative point are electric field lines. In actuality, positive charges are where electric fields begin and negative charges are where they end. Field lines never cross one another, too. If they do, it suggests that the electric field there is moving in two different directions.

Explanation:

Given:

          $Given, Square A B C D \\\\There \ are \ three \ charges \ q_{1}, q_{2} \& q_{3} on A, B and C respectively,\\\\ F_{12} is Force between A \& B \\\\ F_{13} is Force between A \& C .$

Find:

The ratio of magnitudes $F_{12}$ and $F_{13}$ is

Solution:

          Let each side of the square be of "a" length.

          $\begin{gathered}\\\therefore A B=B C=C D=A D=a ---(1)\\ \\\therefore F_{12}=\frac{k q_{1} q_{2}}{a^{2}} \quad \& \quad f_{13}=\frac{k q_{1} q_{3}}{a \sqrt{2}} \text { } \\\quad q_{1}=q_{2}=q_{3}=q --[given \ equal \ charges] \\\\\therefore F_{12}=\frac{k q^{2}}{a^{2}} \quad \& F_{13}=\frac{k q^{2}}{(a \sqrt{2})^{2}} ---(2)\\\\\therefore \quad \frac{F_{12}}{F_{13}}=\frac{k q^{2}}{a^{2}} \times \frac{a^{2} \times 2}{k q^{2}}\text { } \\\\\therefore \quad F_{13} / F_{13}=2\end{gathered}$

Three equal charges $q_{1}, q_{2} \& q_{3}$ are placed at the three corners ABC of a square ABCD. If the force between the charges at A and B is $F_{12}$,  and that between A and C is $F_{13}$  then the ratio of magnitudes $F_{12}$  $F_{13}$ is 2.

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