Drawing electric field lines-Equations or software

Shown below in the diagram are two conducting material connected to a battery source and vacuum OR air is in between them. There will be charges developed on their surfaces. I am interested in finding out the pattern of electric field lines.

Suggest the method to arrive at the equation for the field lines or some software which would plot the field if we could give the charge arragement.

Also, if the potential of the battery is V volts, how to calculate the function of charge developed, with the distance of separation as a variable, and taking the medium of separation as air/vacuum ??

REASON FOR THE DIAGRAM:I am studying about various arc welding processes; and this is important in understanding the process.

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Electric field lines denote the direction of the field at any point. So all you have to do is find the electric field vector at any point, and move an infinitesimal distance along that vector. Keep repeating the process until you reach a negative charge(You should reach one for a conservative field). Now I don't know what approximations you can consider to find the field for the charges you have described – udiboy1209 Aug 13 '13 at 13:23
You'll have to write the code for that - numerical code to solve Laplace's equation $\nabla^2 V = 0$ and electric field would be given by $\vec{E} = -\nabla V$. You can write it in C++ using finite difference method. After getting the results you can plot it using any standard graph plotting software. – guru Aug 13 '13 at 17:07
@guru-thanks a lot; but hiw to plot feikd lines? The equations which you gave me would give me the field but what is the equation for the field lines? – karthikeyan Aug 13 '13 at 20:09