24. Electric Force & Field; Gauss' Law

Two positive point charges are a fixed distance apart. The sum of their charges is Qₜ. What charge must each have in order to

(a) maximize the electric force between them, and

(b) minimize it?

Objects A and B are both positively charged. Both have a mass of 100 g, but A has twice the charge of B. When A and B are placed 10 cm apart, B experiences an electric force of 0.45 N. What is the charge on A?

Two small plastic spheres each have a mass of 2.0 g and a charge of −50.0 nC. They are placed 2.0 cm apart (center to center). What is the magnitude of the electric force on each sphere?

A $-4.00$-nC point charge is at the origin, and a second $-5.00$-nC point charge is on the $x$-axis at $x = 0.800$ m. Find the net electric force that the two charges would exert on an electron placed at each point in part (a). Note: Part (a) asked to find the electric field (magnitude and direction) at each of the following points on the $x$-axis: (i) $x = 0.200$ m; (ii) $x = 1.20$ m; (iii) $x = -0.200$ m.

Suppose that electrical attraction, rather than gravity, was responsible for holding the Moon in orbit around the Earth. If equal and opposite charges Q were placed on the Earth and the Moon, what should be the value of Q to maintain the present orbit? Use data given on the inside front cover of this book. Treat the Earth and Moon as point particles.

What is the direction of the net force on the charge at the center of the square in the following figure?

Two small plastic spheres are given positive electric charges. When they are $15.0$ cm apart, the repulsive force between them has magnitude $0.220$ N. What is the charge on each sphere if one sphere has four times the charge of the other?