The charges and coordinates of two charged particles held fi

The charges and coordinates of two charged particles held fixed in the xy plane are: q1=8.60 C, x1=5.700 cm, y1=5.200 cm, and q2=1.10 C, x2=8.495 cm, y2=12.482 cm, Find the magnitude and direction of the electrostatic force on q2.

What are the x and y coordinates of a third charge q3=4.30 C, if the net electrostatic force on q2 is zero?

Solution

A. F = kq1q2/r^2

r = ((x2-x1)^2 + (y2-y1)^2)^0.5 = ((8.495 - 5.7)^2 + (12.482 - 5.2)^2)^0.5 = 7.79 cm

r(cap) = r(vector)/|r| = (2.795 i + 7.282 j)/7.79 = 0.358 i + 0.934 j

F = 9*10^9*8.6*1.1*10^-12/(7.79*10^-2)^2 = 14.03 N

Fx = 14.03*0.358 = 5.02 i N

Fy = 14.03*0.934 = 13.10 j N

Direction = arctan(13.1/5.02) = 69.03 deg

B.

net F2 = 0

F2 = F12 + F23 = 14.03 + 9*10^9*1.1*4.3*10^-12/r^2 = 0

r = (9*1.1*4.3*10^-3/14.03)^0.5 = 0.055 m = 5.5 cm

The charge must be placed this distance from the second charge, along the line connecting the original charges.

x3 = x2 + r*cos 69.03 = 8.495 + 5.5*cos 69.03 deg = 10.46 cm

y3 = 12.482 + 5.5*sin 69.03 deg = 17.61 cm

This is the correct method to solve this problem, comment below if you find any mistake or have any doubt.