And (a,0) on the x-axis, respectively. Determine the electric field at a point P on the y-axis at a distance r from the origin.

We can use the principle of superposition to find the electric field at point P due to each individual charge, and then add them up to get the total electric field.

First, let's find the electric field due to the charge q at the origin. The electric field at point P due to this charge is given by:

E1 = kq/r^2

where k is Coulomb's constant (k = 9 x 10^9 Nm^2/C^2).

Next, let's find the electric field due to the charge 2q at point (a,0) on the x-axis. The distance from this charge to point P is given by:

d = sqrt(a^2 + r^2)

The electric field at point P due to this charge is given by:

E2 = k(2q)/d^2 = k(2q)/(a^2 + r^2)

Now, we can add up the electric fields due to each charge to get the total electric field at point P:

E = E1 + E2 = kq/r^2 + k(2q)/(a^2 + r^2)

This is the electric field vector at point P, which points along the y-axis. The magnitude of the electric field is given by:

|E| = sqrt(Ey^2) = sqrt((kq/r^2 + k(2q)/(a^2 + r^2))^2)

Note that the electric field is positive if it points in the positive y-direction, and negative if it points in the negative y-direction.