Calculating Electrostatic Force of 3 Point Charges

[Soaring Crane]

Three identical point charges of 2 micro C are placed on the x-axis. The first charge is at the origin, the second to the right at x = 50 cm (.5 m), and the third at the 100 cm (1 m) mark. What are the mag. and direction of the electrostatic force which acts on the charge on the origin?

The answer is 0.18 to the left.

I calculated the magnitude and got 0.18 by:

finding F_12 and F_13, which is .144 N and .036 N, respectively.

F_1 = F_12 + F_13 = .18 N,

where 1 is charge at origin, 2 is charge at .5 m, and 3 is charge at 1m.

Is this even correct at all? Why must F_12 and F_13 be added?
How is the direction to the left?

Thanks.

 

[Poncho]

This is correct. The forces must be added because the electric field adds. You could also calculate the electric field from the 2 and 3 charges and then find the force. The force is to the left because 2 and 3 are to the right of 1 and like charges repell each other.

 

[thepatientmental]

Your calculation is correct. The electrostatic force acting on the charge at the origin is the vector sum of the forces exerted by the other two charges. This is why you add F_12 and F_13 to get F_1.

The direction of the electrostatic force can be determined by using the principle of superposition, which states that the net force on a charge is the vector sum of all individual forces acting on it. In this case, since both F_12 and F_13 are acting in the same direction (to the right), the resulting force F_1 will be in the opposite direction, to the left.

To better visualize this, imagine a tug-of-war between the two charges at .5 m and 1 m, with the charge at the origin caught in the middle. The resulting force on the charge at the origin will be in the direction opposite to the stronger force. In this case, F_12 is stronger than F_13, so the resulting force F_1 will be to the left.

I hope this helps clarify the direction of the electrostatic force and why it must be added. Keep up the good work with your calculations!