Chapter 12.2, Problem 41E

Electric potential function The electric potential function for two positive charges, one at (0, 1) with twice the strength as the charge at (0, –1), is given by

$\phi \left(x,y\right)=\frac{2}{\sqrt{x^2+{\left(y-1\right)}^2}}+\frac{1}{\sqrt{x^2+{\left(y+1\right)}^2}}.$

a.    Graph the electric potential using the window [–5, 5] × [–5, 5] × [0, 10].

b.    For what values of x and y is the potential φ defined?

c.    Is the electric potential greater at (3, 2) or (2, 3)?

d.    Describe how the electric potential varies along the line y = x.