Question

Three point charges q are placed at three vertices of an equilateral triangle of side a. Find magnitude of electric force on any charge due to the other two.

Answer 1

We can solve this using two methods 

1>Using parallelogram law

2>By resolving the components of force

We can use both here since the charges are same and the distance is also same so the components in y-direction will be cancelled out.

And in X- direction will be added.

Answer 2

Given: Three point charges $q$ are placed at three vertices of an equilateral triangle of side $a$.

To find: Magnitude of electric force on any charge due to the other two.

Solution:

Consider an equilateral triangle of side a and three point charges q are placed at three vertices.

We know that,

                Force between two point charges  is given by

                                      $F= \frac{1}{4 \pi \epsilon_0} \frac{q \times q}{a^2}$

                           $F_(net)= \sqrt{ F^2+F^2+ 2FFcos60^ \circ}$

                                      $= \sqrt{3} F$

Putting the value of F

                                $F_(net)= \sqrt{3} \frac{1}{4 \pi \epsilon_0} \frac{q \times q}{a^2}$

Thus, Magnitude of electric force on any charge due to the other two is

                             $F_(net)= \frac{\sqrt{3} }{4 \pi \epsilon_0} ( \frac{q^2}{a^2})$