[BlindMath] I need help with vectors and electric field

[Jonathan Fine]

Hi Abdulqadir

Thank you for this problem, and particularly telling us where you're coming
from. This is most helpful.

The starting point for your problem is Coulomb's inverse square law for
attraction and repulsion between charged particles. It is similar to
Newton's law for gravitational attraction, except that negative masses
don't exist and so there is no repulsion.

Let's start with a simpler problem. Suppose we have two particles A_1 and
A_2 at positions P_1 and P_2, and with charges q_1 and q_2. The size of
force between the two particles is given by the inverse square part of
Coulomb's law. The direction part of Coulomb's law says that the force is
along the straight line joining the two charged particles.

Actually, there are two forces, namely the force on A_1 due to A_2, and the
force on A_2 due to A_1. These two forces are equal and opposite. At this
point it is important to realize that these forces are vectors, which means
that they can be added, and also multiplied by a scalar (i.e. a real
number).

Now suppose we have three particles A_1, A_2 and A_3 at positions and
charges indexed by 1, 2 and 3. Your problem amounts to this. Compute the
force (a vector) on A_3 due to A_1. Similarly compute the force (a vector)
on A_3 due to A_2. Now add these two forces (ie vectors). This gives the
total force exerted on A_3 by the charged particles A_1 and A_2.

There is a detail I've not mentioned. To finish you have to divide by the
charge q_3 on the particle A_3.

I hope this makes the physics part of the application of Coulomb's law
clearer for you. The math part is then computing the magnitude and
direction of the force on A_3 due to A_1, and similar the force on A_3 due
to A_1. This will also require some explanation, which is mostly
mathematics rather than physics.

Would you like me to describe a diagram that might help you?

I hope this helps.

with kind regards

Jonathan