Electric Dipole Moment:
The electric dipole moment is a measure of the separation between positive and negative charges in a system of electric charges and is defined as the product of the magnitude of the charge and the distance between them. It is given by the formula:

p = q * d
where p is the electric dipole moment, q is the magnitude of the charge, and d is the distance between them.

In this case, the magnitude of the charge is 10 micro-coulombs, and the distance between the charges is 5.00 mm. Thus, the electric dipole moment is:

p = (10 * 10^-6 C) * (5.00 * 10^-3 m)
p = 5.00 * 10^-8 Cm

Therefore, the electric dipole moment of the given electric dipole is 5.00 * 10^-8 Cm.

Electric Field at a Point on the Axial Line:
The axial line of an electric dipole is a line passing through the midpoint of the line joining the charges and perpendicular to the line joining the charges. The electric field at a point P on the axial line of an electric dipole is given by the formula:

E = (1 / 4πε₀) * (2p / r³)
where E is the electric field, ε₀ is the permittivity of free space, p is the electric dipole moment, and r is the distance between the point and the midpoint of the line joining the charges.

In this case, the point P is Im away from the midpoint of the line joining the charges. Thus, the distance between the point P and the midpoint of the line joining the charges is:

r = Im + (5.00 / 2) mm
r = (1 * 10^-9 m) + (5.00 / 2 * 10^-3 m)
r = 2.50 * 10^-3 m

Substituting the values in the formula, we get:

E = (1 / 4πε₀) * (2 * 5.00 * 10^-8 Cm / (2.50 * 10^-3 m)³)
E = 2.28 * 10^10 N/C

Therefore, the electric field at point P on the axial line of the electric dipole is 2.28 * 10^10 N/C.

Electric Field at a Point on the Equatorial Line:
The equatorial line of an electric dipole is a line passing through the midpoint of the line joining the charges and perpendicular to the axial line. The electric field at a point P on the equatorial line of an electric dipole is given by the formula:

E = (1 / 4πε₀) * (p / r³)
where E is the electric field, ε₀ is the permittivity of free space, p is the electric dipole moment, and r is the distance between the point and the midpoint of the line joining the charges.

In this case, the point P is Im away from the midpoint of the line joining the charges. Thus, the distance between the point P and the midpoint of the line joining the charges is:

r = Im
r = 1 * 10^-9 m

Substituting the values in the formula, we