Answer to Question #314598 in Electricity and Magnetism for Marcus

Question

Charges of q+ and q- at the two vertices of an equilateral triangle. What can be said of the electric field E and potential V at the unoccupied vertex?

Answer 1

Charges of q+ and q- at the two vertices of an equilateral triangle.

We can say of the electric field E and potential V

Due to charge q₁ at point P

$E_1=\frac{kq_1}{r^2}=\frac{kq}{r^2}$

$E_2=\frac{kq_2}{r^2}=\frac{-kq}{r^2}$

$E_{net}=\sqrt{E_1^2+E_2^2+2E_1E_2cos\phi}$

$\phi=120°$

$E_{net}=\sqrt{E^2+E^2+E^2}=\sqrt{3}E$

$E_{net}=\sqrt{3}\times\frac{kq}{r^2}$

$E\not=0$

$V_{net}=V_1-V_2=0$

Result

$E\not=0,V=0$