Question

Suppose that a charge is positioned at the origin with a magnitude of 5.5 µC, and that a second charge is positioned on the y-axis at y = 8.3 m and has a charge of -2.7 µC. Find the direction of the force on a 1.8 C charge located on the x-axis at x = 13.2 m. Express you answer in degrees relative to the x-axis.

Answer 1

let
q1 = 5.5 micro C
q2 = -2.7 micro C
q3 = 1.8 C

magnitude of force exerted by q1 on q3, F1 = k*q1*q2/d1^2

= 9*10^9*5.5*10^-6*1.8/13.2^2

= 511 N (towards +x axis)

magnitude of force exerted by q2 on q3, F2 = k*q2*q3/d2^2

= 9*10^9*2.7*10^-6*1.8/(13.2^2 + 8.3^2)

= 180 N (below +x axis)

Fnetx = F1x + F2x

= 511 + 180*13.2/sqrt(13.2^2 + 8.3^2)

= 663 N

Fnety = F1y + F2y

= 0 - 180*8.3/sqrt(13.2^2 + 8.3^2)

= -95.8 N

the direction of net force,

theta = tan^-1(Fnety/Fnetx)

= tan^-1(-95.8/663)

= 8.22 degrees below +x axis

(or) 351.8 degrees with +x axis in counter clocwise direction