  The dynamics of a spherical elastic capsule, containing a Newtonian fluid
bounded by an elastic membrane and immersed in another Newtonian fluid, in a
uniform DC electric field is investigated. Discontinuity of electrical
properties such as conductivities of the internal and external fluid media as
well as capacitance and conductance of the membrane lead to a net interfacial
Maxwell stress which can cause the deformation of such an elastic capsule. We
investigate this problem considering well established membrane laws for a thin
elastic membrane, with fully resolved hydrodynamics in the Stokes flow limit
and describe the electrostatics using the capacitor model. In the limit of
small deformation, the analytical theory predicts the dynamics fairly
satisfactorily. Large deformations at high capillary number though necessitate
a numerical approach (Boundary element method in the present case) to solve
this highly non-linear problem. Akin to vesicles, at intermediate times, highly
nonlinear biconcave shapes along with squaring and hexagon like shapes are
observed when the outer medium is more conducting. The study identifies the
essentiality of parameters such as high membrane capacitance, low membrane
conductance, low hydrodynamic time scales and high capillary number for
observation of these shape transitions. The transition is due to large
compressive Maxwell stress at the poles at intermediate times. Thus such shape
transition can be seen in spherical globules admitting electrical capacitance,
possibly, irrespective of the nature of the interfacial restoring force.
