Three point charges are arranged along the x-axis. Charge q 1 = +3.00 ìC is at the origin, and charge q 2 = -5.00 ìC is at x = 0.200 m . Charge q 3 = +8.00 ìC . Where is q 3 located if the net force on q 1 is 7.00 N in the −x direction?

32 Answer

To find the location of q3, we need to calculate the net force acting on q1 and then determine where q3 must be located in order to produce that net force.

The net force acting on q1 is given by Coulomb's law:

F = k * |q1 * q3| / r^2

where F is the net force acting on q1, k is the Coulomb's constant (9 × 10^9 N·m^2/C^2), q1 and q3 are the charges of q1 and q3 respectively, and r is the distance between them.

Since the net force is given as 7.00 N in the −x direction, we know that the force is negative. This implies that q3 is on the negative side of the x-axis (to the left of the origin). Now we can solve for the location of q3.

|F| = k * |q1 * q3| / r^2

Substituting the given values:

7.00 N = (9 × 10^9 N·m^2/C^2) * |(+3.00 × 10^(-6) C) * (8.00 × 10^(-6) C)| / r^2

Simplifying:

7.00 N * r^2 = (9 × 10^9 N·m^2/C^2) * (3.00 × 10^(-6) C) * (8.00 × 10^(-6) C)

r^2 = [(9 × 10^9 N·m^2/C^2) * (3.00 × 10^(-6) C) * (8.00 × 10^(-6) C)] / 7.00 N

r^2 = 2.74 m^2

Taking the square root of both sides:

r ≈ 1.65 m

Therefore, q3 is located approximately 1.65 m to the left of the origin on the x-axis.