Question

1. A particle of charge 2 μC is located at the origin. A second particle of charge 5 μC is located at the coordinates (2.35,3.24)(2.35,3.24) in cm. What is the magnitude of the electric force between the particles?
2. What are the x and y components of the electric force acting on the particle at the point (2.35,3.24)(2.35,3.24)?
3. Four identical particles with charge 3 μC are located at the corners of a square. The square's sides are 3 cm in length. A fifth particle of charge 6 μC is placed directly at the center of the square. What is the magnitude of the total electric force on any one of the four particles at the corners?
4. If you could adjust the charge of the particle at the center, what should you choose so that the net electric force on any of the corner particles is zero?

Answer 1

Electric force (Coulombic force) between two charged particle of charge q and Q and separated by a distance 'r' is given by

                                                    

Where, k = 9 x 10⁹ Nm²/C²

1.

In this problem, q = 2 x 10^-6 C , Q = 5 x 10^-6 C, and the separation between them is

                                                  

So, the force between two charged particle is

                                                 

2. The position vector from origin to that point can be written as

                                  

Angle made by this vector with positive x-axis is

                                            

The force between the two particles will act along the position vector. So, the force on particle at (2.35, 3.24) can be written as

                                         

                                             

                                             

So, the x-component of electric force acting on the particle at (2.35, 3.24) is 33 N and y component of the force is 45.5 N.

Please upload the second question separately.

For any doubt please comment.