Calculation of force exerted on Q by Q1

Given:
- Charge Q1 = 3x10^-4 C located at M(1,2,3)
- Charge Q2 = -10^-4 C located at N(2,0,5)

To calculate the force exerted on Q by Q1, we need to use Coulomb's law which states that the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

Step 1: Calculate the electric field due to Q1 at the position of Q.

The electric field at a point P due to a point charge Q1 located at a point O is given by:
E = (1/4πε) * (Q1/r^2) * u

Where,
ε = Permittivity of free space = 8.85x10^-12 F/m
r = distance between Q1 and P
u = unit vector pointing from Q1 towards P

In this case, the position of Q is not given, so let's assume that Q is located at point A(x,y,z).

The distance between Q1 and Q is given by:
r = √[(x-1)^2 + (y-2)^2 + (z-3)^2]

The unit vector u pointing from Q1 towards Q is given by:
u = [(x-1)i + (y-2)j + (z-3)k] / r

Therefore, the electric field at point A due to Q1 is given by:
E1 = (1/4πε) * (Q1/r^2) * [(x-1)i + (y-2)j + (z-3)k] / r

Step 2: Calculate the force exerted on Q by Q1.

The force F exerted on a charge Q due to an electric field E is given by:
F = Q * E

In this case, the charge Q is not given, so let's assume that Q has a charge of Q3 C.

Therefore, the force exerted on Q by Q1 is given by:
F1 = Q3 * E1

Substituting the values of Q1, Q3, r, and u in the above equation, we get:
F1 = (1/4πε) * (Q1 * Q3 / r^2) * [(x-1)i + (y-2)j + (z-3)k] / r

Step 3: Calculate the numerical value of the force.

Substituting the values of Q1, Q3, r, and u in the above equation, we get:
F1 = (1/4πε) * (3x10^-4 * Q3 / r^2) * [(x-1)i + (y-2)j + (z-3)k] / r

Assuming that Q is located at point A(4,5,6) and has a charge of Q3 = 2x10^-4 C, we get:
r = √[(4-1)^2 + (5-2)^2 + (6-3)^2] = √27
u = [(4-1

If Q1 = 3 × 10-4 C is located at M (1,2,3) and Q2 = -10-4C is located at
N(2,0,5) in vacuum, find the vector force on Q2 by Q1 using Coulomb’s
law