1. Consider placing two point charges on an x-y plane, the firstcharge, q1, at (x1, y1), and the second charge , q2, at (x2,y2).
2. Derive an expression for the electric potential and field atany arbitrary point (x, y) in terms of q1, q2, x1, x2, y1 andy2.
3. Choose some reasonable values for q1, q2, x1, x2, y1 and y2and make a rough sketch of what you expect the electricpotential/field to look like. Your picture doesn’t necessarily haveto be correct, but you should include some justification for whyyour sketch looks the way it does. 4. Use SageMath to draw theexact electric potential and field using the expression derivedabove. Below is an example. x, y = var(\"x y\") g = Graphics() g +=contour_plot(1.5 + 0.2*x*y, (x, -4, 4), (y, -4, 4), fill=False,cmap=\"jet\", labels=True, contours=[0, 1, 2, 3, 4],label_fontsize=14) g += plot_vector_field((y/2, -x/2) , (x, -4, 4),(y, -4, 4)) g.show() Your final result should look something likethe figure below. Note how you can clearly see the two pointcharges at (1, 2) and (2, 1.5).
