`BeF_2` has zero dipole moment where as `H_2 O`has a dipole moment because

Explanation

Dipolemoment is the product of the magnitude of the charge and the distance between the centres of positive and negative charges. It is designated by `mu`.
Dipolemoment `(mu)` = Charge (Q) `xx` distance (r) between the charges. Units of dipolemoment are Debye units (D)
In `BeF_(2)` molecule the Be-F bonds have dipolemoment due to the difference in the electronegativities of Beryllium and fluorine.
`{:(F "___ "Be "___"F),(larr" "rarr):}`
But in polyatomic molecules the dipolemoment of a molecule is the vecotr sum of the dipolemoments of various bonds.
In the case of `BeF_(2)` the dipolemoment becomes zero because the two equal bond dipoles point in opposite direction and cancel the effect each other.
`{:(F"____"Be"____"F),(larr" "rarr):}` Bond dipoles in `BeF_(2)`
Total dipolemoment in `BeF_(2)`