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The recent discovery of electro-active polymers has shown great promises in the field of soft robotics, and was logically followed by experimental, numerical and theoretical developments. Most of these studies were concerned with systems entirely covered by electrodes. However, there is a growing interest for partially active polymers, in which the electrode covers only one part of the membrane. Indeed, such actuation can trigger buckling instabilities and so represents a route toward the control of 3D shapes. Here, we study theoretically the behaviour of such partially active electro-active polymer. We address two problems: (i) the electrostatic elastica including geometric non-linearities and partially electro-active strip using a variational approach. We propose a new interpretation of the equations of deformation, by drawing analogies with biological growth, in which the effect of the electric voltage is seen as a change in the reference stress-free state. (ii) we explain the nature of the distribution of electrostatic forces on this simple system, which is not trivial. In particular we find that edge effects are playing a major role in this problem.