Question

3 charges, 2 of +2.25nC and one of -3nC are placed at the vertices of an equilateral triangle with sides of length 10um. Place the negative charge on the negative axis, one positive charge on the positive x axis, the other positive charge on the positive y axis and the point of interest at the origin, half way between the positive and negative charge. What is the electric field at the origin?

Answer 1

let q1 = -3 nC (at -x axis)

q2 = +2.25 nC (at +x axis)

q3 = +2.25 nc (at +y axis)

let r1,r2 and r3 are the distance from q,q2 and q3 to origin.

r1 = r2 = 10/2 = 5 micro m

r3 = sqrt(10^2 - 5^2) = 8.66 micro m

E12 = E1 + E2

= k*q1/r1^2 + k*q2/r2^2

= 9*10^9*3*10^-9/(5*10^-6)^2 + 9*10^9*2.25*10^-9/(5*10^-6)^2

= 1.89*10^12 n/C (TOWARDS -X AXIS)

E3 = k*q3/r3^2

= 9*10^9*2.25*10^-9/(8.66*10^-6)^2

= 2.7*10^11 N/c (towards -y axis)

Enet = sqrt(E12^2 + E3^2)

= sqrt(1.89^2 + 0.27^2)*10^12

= 1.9*10^12 N/c <<<<<<<<<<<<<<<<<<<<<<<-----------Answer