Determining the Location of q3 to Satisfy the Net Force on q1

Consider three point charges arranged along the x-axis. Charge q1 3.00 μC is at the origin (0,0), charge q2 -5.00 μC is at x0.200 m, and a third charge q3 -8.00 μC needs to be located somewhere on the x-axis such that the net force on q1 is 7.00 N in the – x-direction.

Step 1: Calculate the Force on q1 Due to q2

Let's begin by calculating the electrostatic force F2 on q1 due to charge q2. The formula for the force between two point charges is given by Coulomb's law:

F k * q1 * q2 / r^2

Given:

F2 8.99 * 10^9 * (3.00 * 10^-6 * -5.00 * 10^-6) / (0.200)^2

F2 3.375 N in the x direction

Step 2: Determining the Location of q3

For the net force on q1 to be 7.00 N in the – x-direction, the force exerted by q3 on q1 must be in the – x-direction and must cancel out the force in the x-direction due to q2.

Let x be the distance of q3 from the origin (0,0).

The force based on Coulomb's law due to q3 on q1 is:

F k * q1 * q3 / x^2

Given:

-7.00 8.99 * 10^9 * (3.00 * 10^-6 * -8.00 * 10^-6) / x^2

-7.00 -21.576 / x^2

x^2 21.576 / 7.00 3.082

x √3.082 1.755 m

Step 3: Verify the Net Force

We can verify this by calculating the force due to q3 on q1.

F3 -10.375 N

The net force on q1 is:

Fnet F2 F3 -3.375 -10.375 -7.00 N (in the -x direction)

Conclusion

We have determined that the third charge q3 must be located at x -1.755 m to satisfy the condition that the net force on q1 is 7.00 N in the – x-direction. This result is consistent with our calculations.