Question

Why is the dipole moment of $C{{H}_{4}}$ zero?

Answer 1

Hint: A dipole moment can be shown in those compounds in which separation of charges can be seen. Therefore we can say that dipole moment arises in ionic bonds as well as in covalent bonds. Dipole moments also occur due to the difference in electronegativity between two chemically bonded atoms.

Complete answer:
A bond dipole moment generally measures the polarity of a chemical bond between two atoms in a molecule. It gives us the concept of electric dipole moment which is generally used to measure the separation of negative and positive charges in a system. Dipole moment is a vector quantity i.e. it has both magnitude as well as direction. Due to the property of a vector quantity it can also be zero as two oppositely charged bond dipoles can cancel each other.

Dipole moment also depends upon the structural properties of any compound or we can say on its bond angle. For symmetrical structures bond angles will be zero while for unsymmetrical structures it shows some value. 
In the above example $C{{H}_{4}}$ molecule show zero dipole moment because it is tetrahedral in shape and each bond pair are at equal distance which means these are symmetrically arranged hence each dipole moment of bond balance each other. Hence it has zero dipole moment.
Note: A dipole moment can be calculated as the product of the magnitude of the charge and the distance between the centers of the positive and negative charges. It is represented by the Greek letter$\mu $. Mathematically it is represented as: $\mu = Q\times r$ where Q is charged and d is distance.