The answers are marked in red, but can you please explain how to get 2 and 3? Fo

Question

The answers are marked in red, but can you please explain how to get 2 and 3?

Four charges are on the four corners of a square. Q,-+5 C, Qs--10?C, Q,-+5?C, Q4--10?C. The side length of each side of the square is 3 m. Qi Q2 1) What is the direction of the force on Qi due to ONLY Q4? (a) up (b) down (c) left (d) right e zero Q4 Q3 2) What is the x-component (horizontal component) of the NET force on Qi due to the other three charges? (positive is to the right) (a) 0.05 N (b) 0.041 N (c) 0N (d) -0.041N (e) -0.05 N 3) What is the y-component (vertical component) of the NET force on Qi due to the other three charges? (positive is up) (a) 0.05 N (b) 0.041 N (c) 0N (d) -0.041 N (e) -0.05 N

Explanation / Answer

distacne between q1 qnd q3 is r13 = 3*sqrt(2) = 4.242 m

force between two point charges

f = kq1q2/r^2

a) q4 is negative so force acting on q1 is down wards

b) force between q1 and q2

f12 = 9*10^9*5*10*10^-12/3^3 = 50*10^-3 N

direction along the positive x axis

f13 = 9*10^9*5*5*10^-12/(3*sqrt(2))^2

f13 = 12.5*10^-3 N

f13 makes 135 degrees with the x axis

f13x = 12.5*10^-3cos(135) = -8.84*10^-3 N

fx = (50-8.84)*10^-3 = 41.2*10^-3 N

fx = 0.0412 N

c) f14 = 9*10^9*5*10*10^-12/9 = 50*10^-3 N acting negative y axis

f13y = f13sin135 = 8.84*10^-3 N

fy = 8.84*10^-3-50*10^-3 = -0.0412 N

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