Two hard rubber spheres, each of mass m - 14.9 g, are rubbed with fur on a dry day and are then suspended with two insulating strings of length L= 5.25 cm whose support points are a distance d = 3.06 cm from each other as shown in the figure below. During the rubbing process, one sphere receives exactly twice the charge of the other. They are observed to hang at equilibrium, each at an angle of 0-10.4° with the vertical. Find the amount of charge on each sphere. (Enter your answer smallest to largest.) C 711

Two identical metallic spheres are suspended as bobs of a simple pendulum. The spheres come to equilibrium when given a charge of +7.5 nC, with each string making an angle of 5° with the vertical. The string is 0.5 m long. Find the electric force between the spheres.

The drawings show three charges that have the same magnitude but may have different signs. In all cases the distance d between the charges is the same. The magnitude of the charges is |q|=7.3 µC, and the distance between them is d=3.2 mm. Determine the magnitude of the net force on charge 2 for each of the three drawings. 1 (a) F= i (b) F= i (c) F= i +q 2 (a) +q 3 +q 1 +q 2 (b) +q 3 > > +q 1 21 Id +q 3

Two identical spheres are attached to silk threads of length L=0.60 m and hung from a common point as shown in the figure. Each sphere has a mass m=7.0 g. One sphere is given a charge q1, and the other is given a different charge q2, this causes the spheres to separate so that when the spheres are in equilibrium, each thread makes an angle = 20 degrees with the vertical. A small wire is then connected to the spheres, allowing charge to be transferred from one sphere to the other until the two spheres have equal charges, the wire is then removed. Each thread now makes an angle = 30 degrees. Determine the original charge (in micro-coulomb) of q1.

Three dots are resting on the vertices of a triangle. The sides of the triangle have a length of a = 0.68 m, as shown. Two of the dots (S1 and S3) have +6.5 µC charge, while the other (S2) has −6.5 µC charge. (a) Find the direction of the net force on the third dot (S3) in degrees counterclockwise from the +x-axis.   (b) Find the direction of the net force on the third dot (S3) when it is moved to the origin in degrees counterclockwise from the +x-axis.

The drawings show three charges that have the same magnitude but may have different signs. In all cases the distance d between the charges is the same. The magnitude of the charges is lql=7.9 µC, and the distance between them is d=6.4 mm. Determine the magnitude of the net force on charge 2 for each of the three drawings. 1 (a) F = i (b) F= i (c) F = i +q 2 (a) +q 3 +q 1 +q 2 (b) +q 3 +q 1 < (c) 21 |d I +q 3

An electric dipole in a uniform horizontal electric field of magnitude 2.5 x 105 N/C is currently at rest and makes an angle 0 = 17° with the E field. The charges have equal magnitudes q = 3.0 µC and are separated by a fixed distance 2a = 2.0 x 10-8 m. When released, the dipole swings clockwise about an axis through its center, with no friction or other damping, until it next comes to rest. At that moment, what angle will the dipole make with the E field? 2a a) 11° b) 14° c) 17° d) 21° e) 24°

(a) A physics lab instructor is working on a new demonstration. She attaches two identical iron spheres with mass m = 0.190 g to filaments of length L as shown in the figure. L. Both spheres have the same charge of 7.60 nC, and are in static equilibrium when 0 = 5.20°. What is L (in m)? Assume the filaments are massless. 0.31 (b) What If? The charge on both spheres is increased until each filament makes an angle of 0 = 10.4° with the vertical. If both spheres have the same electric charge, what is the charge (in nC) on each sphere in this case? 2.16E-8 Use the same reasoning as in part (a), only now, use the length found in part (a) and the new angle to solve for the charge. nC

Two metal spheres of identical mass m 3.60 g are suspended by light strings 0.500 m in length. The left-hand sphere carries a charge of 0.885 μC, and the right-hand sphere carries a charge of 1.59 μC. What is the equilibrium separation between the centers of the two spheres? m =

The drawings show three charges that have the same magnitude but may have different signs. In all cases the distance d between the charges is the same. The magnitude of the charges is lal-9.4 µC, and the distance between them is d-4.1 mm. Determine the magnitude of the net force on charge 2 for each of the three drawings. (a) F-i (b) Fi (c) F= i (M) (0 +9