In Figure 18.17a the charges on the two metal spheres and the ebonite rod create an electric field E at the spot indicated. This field has a magnitude of 2.0 N/C and is directed as in the drawing. Determine the force on a charge placed at that spot, if the charge has a value of (a) q₀=+18×10^–8 C and (b) q₀=–24×10^–8 C.

Figure 18.17  The electric field E that exists at a given spot can exert a variety of forces. The force exerted depends on the magnitude and sign of the charge placed at that spot. (a) The force on a positive charge points in the same direction as E, while (b) the force on a negative charge points opposite to E.

Reasoning  The electric field at a given spot can exert a variety of forces, depending on the magnitude and sign of the charge placed there. The charge is assumed to be small enough that it does not alter the locations of the surrounding charges that create the field.

Solution

(a)	The magnitude of the force is the product of the magnitudes of q0 and E:  (18.2)  Since q0 is positive, the force points in the same direction as the electric field, as part a of the drawing indicates.
(b)	In this case, the magnitude of the force is  (18.2)  The force on the negative charge points in the direction opposite to the force on the positive charge—that is, opposite to the electric field (see part b of the drawing).