Question $6$

Three charges, $+5Q,-5Q,$ and $+3Q$ are located on the $y-$axis at $y=+4a,y=0,$ and $y=-4a,$ respectively. The point P is on the x $-$axis at $x=3a.$

a$)$ How much energy did it take to assemble these charges?

b$)$ What are the $x,y,$ and z components of the electric field vec$(E)$ at P $?$

c$)$ What is the electric potential V at point P $,$ taking $V=0$ at infinity?

d$)$ A fourth charge of $+Q$ is brought to $P$ from infinity. What are the $x,y,$ and $z$ components of the force vec$(F)$ that is exerted on it by the other three charges?

e$)$ How much work was done $($by the external agent$)$ in moving the fourth charge $+$Q from infinity to $P?$