Question

A square of side length v2D has charge +Q on three of the cormers and charge -Q on the bottom right corner. A charge +q is placed at the exact centre of the square. What is the magnitude of the net force on this charge? Enter your expression n terms of k.Q q, and D Use an asterisk *, t indicate mult plication For example, 2ソ(z) a * z * z + b "(e. z + d. b *tan a. ) or e a%)

Answer 1

The situation in the question can be shown by this diagram,

here ,

According to the question, AB = BC = CD = DA = a and OA = OB = OC = OD = r.

The value of r can be calculated using some basic mathematics.

+Q I a/2 2 tq +Q

From the figure,

Putting the value of a, we get

The electrostatic force between two charges is given by

  

Where, k is a constant

q₁ and q₂ are two charges

and r is separation between the charges

This force always acts along the line connecting the two charges.

Two same charges (both +ve or both -ve) repel each other while two opposite (i.e. one +ve and one -ve) charges attract each other.

Now, we will calculate the force on the charge +q (at O) due to all other charges (i.e. charge at A, B, C & D).

Magnitude of force due to charge at A is

   acting towards the C.

Magnitude of force due to charge at B is

   acting towards the D.

D2

Magnitude of force due to charge at C is

   acting towards the A.

Magnitude of force due to charge at D is

  

This negative sign is indicating that the force is acting towards the D.

Hence, all forces have same magnitude.

But, the force on the charge q (at O) due to the charges at A and C will cancel out each other because they are acting in opposite direction of each other.

And the force on +q charge due to charge at B and D is acting towards the D. So, the magnitude of net force acting on the +q charge (charge at O) is

    

za za za

For any doubt please comment and please give an up vote. Thank you.