Three point charges are placed at distances of d , 2 d , and 3 d from a point P. The particle that is 2 d away from P has a charge of 6 q . From the options given, assign charges to the remaining two point charges such that the potential at point P is zero.

at d the charge will be 3q and at 3d it will be 9q

Explanation:

for V=Vp-V2d

V=KQ/d=K*6q/2d=3kq/d for potential to 2d at 6q be zero the Vp will equal 3kq/d; hence at d, Q=3q and at 3d, Q=9q

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west

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