(a) The charges and coordinates of two charged particles heldfixed in the xy pla

Question

(a) The charges and coordinates of two charged particles heldfixed in the xy plane are: q1=9.70 C,x1=-7.100 cm, y1=7.800 cm, andq2=6.50 C, x2=-5.166 cm,y2=17.305 cm, Find the magnitude anddirection of the electrostatic force on q2.
I already have the answer forthis:
6.0254×101 N7.8500×101 deg (b) What are the x and y coordinates of a thirdcharge q3=9.50 C, if the net electrostaticforce on q2 is zero? (a) The charges and coordinates of two charged particles heldfixed in the xy plane are: q1=9.70 C,x1=-7.100 cm, y1=7.800 cm, andq2=6.50 C, x2=-5.166 cm,y2=17.305 cm, Find the magnitude anddirection of the electrostatic force on q2.
I already have the answer forthis:
6.0254×101 N7.8500×101 deg (b) What are the x and y coordinates of a thirdcharge q3=9.50 C, if the net electrostaticforce on q2 is zero?

Explanation / Answer

the electrostatic force between chares q1 and q2 is F = k * (q1 * q2/r^2) k = (1/4o) = 9 * 10^9 Nm^2/C^2 q1 = 9.70 C = 9.70 * 10^-6 C q2 = 6.50 C = 6.50 * 10^-6 C r^2 = [(-5.166 - (-7.1))^2 + (17.305 - 7.8)^2]^(1/2) = 94.08m^2 the drection of the elecrostatic force on q2 is tan = (17.305 - 7.8/-5.166 - (-7.1)) =(9.505/1.934) or = tan-1(9.505/1.934) = 78.5oin the direction away from q2. (b)let the coordinates of the third charge q3 = 9.50 Cbe (0,y3) the force between the charges q1 and q2 is F1 = k * (q1 * q2/r1^2) and F2 = k * (q2 * q3/r2^2) when the net electrostatic force on q2 is zero then F1 + F2 = 0 or k * (q1 * q2/r1^2) + k * (q2 * q3/r2^2) = 0 or (q1 * q2/r1^2) = -(q2 * q3/r2^2) or (q1/r1^2) = -(q2/r2^2) or (r1^2/r2^2) = -(q1/q2) or [((0 - (-0.71))^2 + (y3 - 7.8)^2)/((0 - (-5.166))^2 + (y3 -17.305)^2] = -(9.70 * 10^-6/6.50 * 10^-6) solving the above equation for y3 we get the result.

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