An equilateral triangle with a side of length a has point electric charges q , 2q and 3q, respectively, at its vertices. Calculate the electric field and electric potential at the center of the equilateral triangle in terms of Coulomb's constants, a and q.

A capacitor is composed of two metal plates. The two plates have the dimensions L = 0.11 m and W = 0.56 m. The plates have a distance between them of d = 0.1 m, and are parallel to each other.  Part (a)  The plates are connected to a battery and charged such that the first plate has a charge of q. Write an expression for the magnitude of the electric field, |E|, halfway between the plates.  Part (b)  Input an expression for the magnitude of the electric field, |E2|, just in front of plate two.  Part (c)  If plate two has a total charge of q = -1 mC, what is its charge density, σ, in C/m2?

A solid cylindrical conductor of radius a is surrounded by a concentric cylindrical shell of inner radius b. The solid cylinder and the shell carry charges Qand-Q, respectively. Assuming that the length L of both conductors is much greater than a or b, what is the potential difference between the two conductors? ○a. V = -2k²ln(²/2) ○b. V = -2k²ln() OC. V = -k²ln(4) O d. V = -kln()

In the early 1900s, Robert Millikan used small charged droplets of oil, suspended in an electric field, to make the first quantitative measurements of the electron’s charge. A 0.70-μm-diameter droplet of oil, having a charge of +e, is suspended in midair between two horizontal plates of a parallel-plate capacitor. The upward electric force on the droplet is exactly balanced by the downward force of gravity. The oil has a density of 860 kg/m3, and the capacitor plates are 5.0 mm apart. What must the potential difference between the plates be to hold the droplet in equilibrium?