As the sheath is mainly defined by the plasma potential profile and you have the rule of superposition for potential energy, the resulting potential profile should just be the sum of both potentials in each point of space.

thanks johannes gruenwald,

but what will be the direction of potential gradient or electric field in the superposition region.?  since, potential is a scalar quantity so we can take an superposition values but the potential gradient direction is diff. for both sheaths. for planar it is in z direction and for object these are in two directions ( around object in radial and below in -z direction). so please help me to use the superposition law.  

The gradient is a mathematical operation onto a scalar field. So, you have to calculate the net potential profile of the two sheaths and apply the gradient to it.

You have to agree on one coordinate system, so you will have to make a transformation, either from cylindrical to cartesian coordinates or vice versa.

You can even measure the potential, as when the z-axis of the cylinder is normal to the surface of the plane electrode, you can measure in radial direction as the contribution from the plane surface will (ideally) just be constant in this direction.

Mangilal, your statement "if we put a cylindrical object in this plasma then it sits on a potential to balance the electron and ion current." implies that your cylindrical probe is floating  (floating = no net current, i.e. electron and ion current cancel or "balance").  The sheath around the probe forms to accomplish exactly this: making the electron and ion currents cancel.  

This is not the case for the sheath at the cathode of your glow discharge.  There, the sheath establishes itself  to get the right current to the cathode, i.e. for the current determined primarily by the circuit of the discharge.   

Now, the sheaths will always adjust to fulfill their functions.  When these two sheaths connect you get a complicate situation as you combine a planar geometry (cathode) with a cylindrical geometry (probe).  The situation is 3D and may be treated in 2D as one could still apply axial symmetry with the probe axis as the axis of symmetry.   As the probe's sheath touches the cathode sheath, the sheath will connect but assume a complicate shape and internal potential structure is which determined by their function of controlling currents.

Finally, I'm not so sure the statement "potential profile will follow the exponential rule from the surface to the sheath edge" is applicable at the pressure of a glow discharge.  There are collisions in the sheath at glow discharge pressures.  You cannot assume that the rules of a collisionless sheath apply.