Three point charges are arranged along the x-axis. Charge q1 = +2.75 µC is at the origin, and charge q2 = -6.00 µC is at x = 0.220 m. Charge q3 = -7.00 µC. Where is q3 located if the net force on q1 is 6.75 N in the −x-direction?
I sketched q3 between q1 and q2
look at left forces
F from 3 is left
C (6*7)/(.22-x)^2
F from 1 is also left
C (2.75*7)/(x)^2
so
C [42/(.22-x)^2 + 19.25/x^2] = 6.75
C is µ*k
sorry
µ^2 k
well, if you have two negative charges to the right of the positive, the force on the positive charge is to the right. You want it to the left, which means the q3 has to be in -x region.
netF=k( q1q2/.220^2 -q1Q3/x^2)
netF=k*10^-12(2.75*6/.220^2-2.75*7/x^2)
Then proceed to a solution. Compare this solution with yours, I do not see how you got your denominators...
To find the location of charge q3, we need to calculate the distance between q3 and the origin (point O).
Let's break down the problem into steps:
Step 1: Find the distance between q1 and q3
The net force on q1 due to q3 can be calculated using Coulomb's law:
F13 = k |q1| |q3| / r13^2
where k is the electrostatic constant, q1 and q3 are the magnitudes of the charges, and r13 is the distance between them.
Given that F13 = -6.75 N and q1 = +2.75 µC, we can rearrange the equation to solve for r13:
r13^2 = k |q1| |q3| / F13
r13^2 = (9.0 × 10^9 N m^2/C^2) (2.75 × 10^-6 C) (7.00 × 10^-6 C) / 6.75 N
r13^2 = 6.8 × 10^-4 m^2
Taking the square root of both sides:
r13 = 0.026 m
Step 2: Find the position of q3
Since q1 is at the origin (x = 0) and q2 is at x = 0.220 m, the distance between q3 and the origin can be calculated as follows:
Distance from q1 to q2 = 0.220 m
Distance from q2 to q3 = r13 = 0.026 m
Therefore, the position of q3 is located at:
x = 0.220 m + 0.026 m
x = 0.246 m
So, q3 is located at x = 0.246 m.