Two point charges q and -2q are kept 'd' distance apart . Find the location of point relative to charge 'q' at which potential due to this system of charges is zero.

To find the location of the point relative to charge 'q' where the potential due to this system of charges is zero, we can use the concept of electric potential.

The electric potential at a point due to a point charge is given by the equation:

V = k * q / r

Where:
- V is the electric potential
- k is the Coulomb's constant (k = 8.99 * 10^9 Nm^2/C^2)
- q is the charge
- r is the distance between the charge and the point

In this case, we have two point charges: q and -2q, located 'd' distance apart. We want to find the location where the potential is zero relative to charge 'q'.

Let's assume the distance between the location of interest and charge 'q' is x. Therefore, the distance between the location of interest and charge '-2q' would be (d - x).

The potential due to charge 'q' at the location would be Vq = k * q / x.
The potential due to charge '-2q' at the location would be V-2q = k * (-2q) / (d - x).

Since we want the total potential to be zero, we can set Vq + V-2q = 0 and solve for x.

k * q / x + k * (-2q) / (d - x) = 0

Simplifying the equation:

q / x - 2q / (d - x) = 0

Multiplying through by x(d - x) to eliminate the denominators:

q(d - x) - 2qx = 0

qd - qx - 2qx = 0

qd - 3qx = 0

qd = 3qx

Dividing both sides by q:

d = 3x

Finally, solving for x:

x = d / 3

Therefore, the location of the point relative to charge 'q' where the potential is zero is at a distance of d/3 from charge 'q'.