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The animation shows the equipotential contours around two charged spheres. Restart. You can change the charge of particle A by using the text box. As you click-drag your mouse around the screen, you can see the magnitude of the electric field as well as the electric potential (position is given in meters, electric potential is given in volts, and electric field strength is given in newtons/coulomb). The zero point of electric potential is infinity (far away from the charge distribution).

Change the value of the charge of A so that the charges are equal. Where (if anywhere on the screen) is the electric field zero? Where is the electric potential zero? What happens if the charges have equal and opposite charge? In this case, where is the electric field zero? Where is the electric potential zero?

What happens to the equipotentials if you make charge A more positive? What happens to the equipotentials as you make charge A more negative?

The electric potential due to one point charge is proportional to the charge divided by the distance to the charge (V = k q/r). When charge A is equal to charge B (in magnitude and sign), where do you need to put a third charge, negative but with the same magnitude of charge, in order for the potential in the middle of A and B [at point (0, 0)] to be zero? Add a charge and move it to the correct spot to check your answer. Is there more than one place you can put this charge? The electric potential of the original two charges, as measured at the origin, is V = k(2Q), since r = 1 m. The electric potential of the third charge must be V = -k(2Q) to cancel this electric potential at the origin. Therefore, the third charge must be placed at any position that is a distance of r = 0.5 m from the origin.

Illustration authored by Anne J. Cox.