Three identical point charges, each with a charge equal to q, lie in the xy plan

Question

Three identical point charges, each with a charge equal to q, lie in the xy plane. Two of the charges are on the axis at y = -a and y = +a, and the third charge is on the x axis at x = a. Find the potential as a function of position along the x axis. (Use any variable or symbol stated above along with the following as necessary: k for the Coulomb's constant, and q for the charge.) Use the Part (a) result to obtain an expression for E_x(x), the x component of the electric field as a function of x. (Use any variable or symbol stated above along with the following as necessary: k for the Coulomb's constant, and q for the charge.)

Explanation / Answer

a) for x>a
V =2*potential due to the charges on Y(as the case is symmetric) +due to those on X
=2*kq/?(x2+a2)+kq/(x-a)

for(x<a) V=2*kq/?(x2+a2)+kq/(a-x)

b)E(x>a)=-dV/dx

-kq*2x/(x2+a2)1.5+kqln((x-a)

E(x<a)=-kq*2x/(x2+a2)1.5+kqln(a-x)

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