An electric dipole (any pair of oppositely charge point particles) lies on the x-axis, consisting of a - 2.5nC charge at x = -10 cm, and a +2.5nC charge at x=10cm. Find the electric field (a) on the x-axis, at the point (20,0) and (b) on the y-axis, at point (0,10).

To find the electric field at a point, you can use the formula for the electric field due to an electric dipole:

E = k * (p / r^3)

where:
- E is the electric field
- k is the electrostatic constant (9 x 10^9 Nm^2/C^2)
- p is the dipole moment
- r is the distance from the point to the dipole

The dipole moment p is defined as the product of the magnitude of the charge and the distance between the charges:

p = q * d

where:
- q is the magnitude of the charge
- d is the distance between the charges

Now, let's calculate the electric field at the given points:

(a) Electric field at point (20,0) on the x-axis:
- The distance from the dipole to the point is 20 cm.
- The dipole moment p is q * d = (2.5 x 10^-9 C) * (20 cm) = 0.05 x 10^-9 C.m.
- Plugging the values into the formula, we get:

E = (9 x 10^9 Nm^2/C^2) * (0.05 x 10^-9 C.m) / (0.2 m)^3

Simplifying the expression, we get:

E = 9 x 10^9 Nm^2/C^2 * 0.25 x 10^-9 C.m / 0.008 m^3
E = 112.5 N/C

Therefore, the electric field at point (20,0) on the x-axis is 112.5 N/C.

(b) Electric field at point (0,10) on the y-axis:
- The distance from the dipole to the point is 10 cm = 0.1 m.
- The dipole moment p is the same as before (0.05 x 10^-9 C.m).
- Plugging the values into the formula, we get:

E = (9 x 10^9 Nm^2/C^2) * (0.05 x 10^-9 C.m) / (0.1 m)^3

Simplifying the expression, we get:

E = 9 x 10^9 Nm^2/C^2 * 0.25 x 10^-9 C.m / 0.001 m^3
E = 2.25 x 10^12 N/C

Therefore, the electric field at point (0,10) on the y-axis is 2.25 x 10^12 N/C.