Problem: Find the potential at point x=0 due to an infinite number of charges each equal to q placed along x-axis at x=1, x=2, x=4, x=8.

Solution:
To find the potential at point x=0 due to this set of charges, we need to use the principle of superposition. According to this principle, the potential at any point due to a set of charges is the sum of the potentials due to each charge.

Step 1: Calculate the potential due to each charge

We can calculate the potential due to each charge using the formula:

V = kq/r

where k is the Coulomb constant, q is the charge, and r is the distance between the charge and the point where we want to find the potential.

For the first charge at x=1, the distance between the charge and x=0 is 1 unit. Therefore, the potential due to this charge is:

V1 = kq/1 = kq

For the second charge at x=2, the distance between the charge and x=0 is 2 units. Therefore, the potential due to this charge is:

V2 = kq/2

For the third charge at x=4, the distance between the charge and x=0 is 4 units. Therefore, the potential due to this charge is:

V3 = kq/4

For the fourth charge at x=8, the distance between the charge and x=0 is 8 units. Therefore, the potential due to this charge is:

V4 = kq/8

Step 2: Find the total potential due to all the charges

The total potential due to all the charges is the sum of the potentials due to each charge. Therefore, the total potential at x=0 is:

V = V1 + V2 + V3 + V4
= kq + kq/2 + kq/4 + kq/8
= kq(1 + 1/2 + 1/4 + 1/8)
= kq(15/8)

Step 3: Simplify the expression

We can simplify the expression by substituting the value of k:

V = (1/4πε₀)q(15/8)
= q/2ε₀

where ε₀ is the permittivity of free space.

Therefore, the potential at point x=0 due to this set of charges is q/2ε₀.