Question

Consider four masses arranged (clockwise from A at the top) in a cross (looks like a giant plus symbol). Each is 1cm from the center of the cross. Mass A has a charge +1𝜇C , mass B has a charge of −1𝜇C , and mass C has a charge of +2𝜇C . At the center the electric field points 30 degrees (Northeast) from the vertical axis.

Is there a formula I need to find the missing value of D? I tried setting opposite ends equal to separate and find D but I cant figure this out or find anything online like it. Thank you.

Answer 1

look at the relative field strengths (at the center) from the individual charges
... they are all one cm away
... so the contribution to the net field is proportional to the charge

north-south is +1 N

east-west is ... D - 1 E

(E-W) / (N-S) = tan(30º)