Three charges are arranged in the (x, y ) plane as shown. What is the magnitude

Question

Three charges are arranged in the (x, y ) plane as shown.

What is the magnitude of the resulting force on the 5 nC charge at the origin?

The value of the Coulomb constant is8.98755×10^9 N·C^2/m^2.Answer in units of N

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y (m) 3 0 5 nC 3 -5 nC 5 -3 -101 2 34 5 What is the magnitude of the result gin? The value of the Coulomb constant is ing force on the 5 nC charge at the 8.98755 × 109 N . C2/m2. Answer in units of N.

Explanation / Answer

let

q1 = -3 nc

q2 = -5 nc

q3 = +5 nc

force exerted by q1 on q3m

F13 = k*q1*q3/d13^2

= 9*10^9*3*10^-9*5*10^-9/(1^2 + 3^2)

= 1.35*10^-8 N

angle made by F13 above +x axis, theta1 = tan^-1(3/1) = 71.6 degrees

force exerted by q2 on q3m

F23 = k*q2*q3/d13^2

= 9*10^9*5*10^-9*5*10^-9/(5^2 + 4^2)

= 0.548*10^-8 N

angle made by F23 below +x axis, theta2 = tan^-1(4/5) = 38.7 degrees

angle between F13 and F23 = 71.6 + 38.7

= 110.3 degrees

net force on q3, Fnet = sqrt(F13^2 + F23^2 + 2*F13*F23*cos(theta))

= sqrt(1.35^2 + 0.548^2 + 2*1.35*0.548*cos(110.3))*10^-8

= 1.27*10^-8 N <<<<<<<-----------Answer

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