Question

A small sphere of charge q+67 pC and mass m-5.4 g is attached to a light string and placed in a uniform electric field e that makes an angle θ-31° with the horizontal. The opposite end of the string is attached to a wall and the sphere is in static equilibrium when the string is horizontal as in the figure shown below. (a) Construct a free body diagram for the sphere. (Submit a file with a maximum size of 1 MB.) This answer has not been graded yet. (b) Find the magnitude of the electric field. N/C (c) Find the tension in the string. (Enter the magnitude of the tension in the string.) If the electric field strength in air exceeds 3.0 x 106 N/C, the air becomes a conductor. Using this fact, determine the maximum amount of charge that can be carried by a metal sphere 2.6 m in radius. (Hint: Review properties of conductors in electrostatic equilibrium. Also, note that the points on the surface are outside a spherically symmetric charge distribution; the total charge may be considered to be located at the center of the sphere.) Need Help? Two small beads having positive charges q1-4q and q2-q are fixed at the opposite ends of a horizontal insulating rod of length d 1.70 m. The bead with charge qi is at the origin. As shown in the figure below, a third small charged bead is free to slide on the rod. At what position x is the third bead in equilibrium?

Answer 1

1. a) The sphere has three forces acting on it: its weight (down), the string tension (presumably to the left) and the electric field which has components that balance out the other two forces (hence equilibrium).

b) E = F / q = 0.103 N / 65 * 10^-6 C = 1584.62 N/C

c)The vertical component of the electrostatic force must equal the weight:
F*sin31º = mg
F = mg / sin31º = 0.0054 kg * 9.8 m/s² / sin31º = 0.103 N

2. Outside the sphere, Gauss’ law says that the electric field is just that of a point charge. That means for a radius r > 2.6 m from the center, the field is

keq

where q is the charge on the sphere. Since we wish for E to exceed 3.0 × 10⁶ N/C