There are two identical rods of length 2a lying along the x-axis with their centers separated by a distance b (b > a). Each rod carries an equal charge of +Q uniformly distributed along their lengths. Please calculate the magnitude of the force exerted by the left rod on the right one.

Let the variable be the position placing on the left rod and the variable placing on the right rod. Here () is the infinitesimal displacement on the left (right) rod. The linear charge density is and the infinitesimal charge can be expressed as . The force exerted on the left rod with an infinitesimal displacement and an infinitesimal charge by an infinitesimal charge is:The total force is obtained through the integration:

In the inner integration, the is a variable and the is a constant so we have the equivalent relation . The above equation leads to: