Question

Given a charge of +q at coordinates (-d,0), -2q at (0,d), and +8q at (2d,0), for d=1.5m and a= 2.7 uC,

a.) What is the potential at the origin?

b.) What is the potential energy of a charge Q= +20 uC if placed at the origin?

Answer 1

a)

$$V=\frac{2.7\cdot10^{-6}}{1.5}-2\frac{2.7\cdot10^{-6}}{1.5}+8\frac{2.7\cdot10^{-6}}{2\cdot1.5}\\V=5.4\cdot10^{-6}\ V$$

b)

$$E=QV\\E=(20\cdot10^{-6})(5.4\cdot10^{-6})=1.08\cdot10^{-10}\ J$$