  Generally the virial theorem provides a relation between various components
of energy integrated over a system. This helps us to understand the underlying
equilibrium. Based on the virial theorem we can estimate, for example, the
maximum allowed magnetic field in a star. Recent studies have proposed the
existence of highly magnetized white dwarfs, with masses significantly higher
than the Chandrasekhar limit. Surface magnetic fields of such white dwarfs
could be more than 10^9 G with the central magnitude several orders higher.
These white dwarfs could be significantly smaller in size than their ordinary
counterparts (with surface fields restricted to about 10^9 G). In this paper we
reformulate the virial theorem for non-rotating, highly magnetized white dwarfs
(B-WDs) in which, unlike in previous formulations, the contribution of the
magnetic pressure to the magnetohydrostatic balance cannot be neglected. Along
with the new equation of magnetohydrostatic equilibrium, we approach the
problem by invoking magnetic flux conservation and by varying the internal
magnetic field with the matter density as a power law. Either of these choices
are supported by previous independent work and neither violates any important
physics. They are useful while there is no prior knowledge of field profile
within a white dwarf. We then compute the modified gravitational, thermal and
magnetic energies and examine how the magnetic pressure influences the
properties of such white dwarfs. Based on our results we predict important
properties of these B-WDs, which turn out to be independent of our chosen field
profiles.
