There are very large numbers of charged particles in most objects. Why, then, don't most

Like charged Styrofoamcups, barmagnets exertforces on one another, as if they possessedinvisible hands that reach across empty space to push and twist. They also exert torques on one another. You may recall from mechanics thatwhen two bodies bumpintoeach other, theyexert equal and opposite contact forces on one another If the forceis directed through the centerof mass of the body then thereis no torque. If theforce is “oblique”itexerts atorque where is the “lever”, the distance between the centerof mass and the point of application of the force, and is the component of the force perpendicularto the lever. We can demonstrate that two barmagnets exert “body centered”forces as well as torques. In this case, the forces and torques are not the result of contact forces, ratherof invisible forces. A charged cup haselectriccharge , and this charge creates aninvisible electricfield in space all around the cup. The electricfield exerts forces on othercharged cups. Similarly, we saythatabar magnethas akind of “magneticcharge”, called the magneticdipole moment . The dipole creates an invisible magneticfield all around the magnet. The field exerts forces and torques on other magnets, and as you will see,it also exerts forces on moving charges! Like the barmagnet, the Earth has a magneticdipole and a magneticfield, and this field exerts atorque on the needle of compass; the needleis tiny bar magnet. An electron has amagneticdipole and amagneticfield. Early experimentersfound that aloop of wire carrying an electriccurrent has amagneticdipole and a magneticfield. It