Rod Bearing +2q W +Q The figure above shows a long, nonconducting, massless rod of length L, pivoted at its center and balanced with a block of weight W at a distance x from the left end. At the left and right ends of the rod are attached small conducting spheres with positive charges q and 2q, respectively. A distance h directly beneath each of these spheres is a fixed sphere with positive charge Q. NOTE: Express your answer in terms of the given variables, use permittivity constant co. (a) Find an equation for the distance x when the rod is horizontal and balanced. x = (b) What value should h have so that the rod exerts no vertical force on the bearing when the rod is horizontal and balanced? h =
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- Let's say two unknown charges are given to you. You do not know their individual charges, but you know that their total charge is 8.00µC. You made a test in the laboratory and found that these two charges push each other away with a force of 0.150 N when separated by 0.500 m. What is the charge of the "higher charge" in units of µC ?Two identical, small insulating balls are suspended by separate 0.21-m threads that are attached to a common point on the ceiling. Each ball has a mass of 7.7 × 10-4 kg. Initially the balls are uncharged and hang straight down. They are then given identical positive charges and, as a result, spread apart with an angle of 50° between the threads. Determine (a) the charge on each ball and (b) the tension in the threads. A F₁Two otherwise identical conducting spheres carry charges of +4.80 µC and –1.00 µC. They are initially a distance L apart. The distance L is much larger than the radii of the spheres. The spheres were brought together, touched, and then returned to their original separation L. What is the ratio of the magnitude of the force on either sphere after they are touched to that before they were touched?
- A very thin glass rod 4 m long is rubbed all over with a silk cloth (see figure below). It gains a uniformly distributed charge +4.2 x 10-6 C. Two small spherical rubber balloons of radius 1.2 cm are rubbed all over with wool. They each gain a uniformly distributed charge of -6.7 x 10-8 C. The balloons are near the midpoint of the glass rod, with their centers 3 cm from the rod. The balloons are 2 cm apart (4.4 cm between centers). Length 4 m (drawing not to scale) 2 cm --- 3 cm Radius 1.2 cm 0.6 cm Part 1 (a) Find the magnitude of the electric field at the location marked by the x, 0.6 cm to the right of the center of the left balloon. i N/C Also calculate the angle the electric field makes with the horizontal. (Take the horizontal to be the +x axis pointing to the right.) i counterclockwise from the +x axis.A pair of unlike charges equal in magnitude and separated by a small distance is known as a dipole. Such a pair is situated on the x axis at equal distances from the origin as shown in the figure below. Use the direction rosette to answer the questions. ΧΑ 8 + * D E B 3 +q -9 5 9 zero magnitude (a) What is the direction of the net electric field at location C due to both charges? 5 X Did you consider the symmetry of the situation? What is the net contribution to the field from the y components of the field from each charge? (b) What is the direction of the net electric field at location D due to both charges? ---Select--- v (c) What is the direction of the net electric field at location E due to both charges? ---Select--- ✓ Additional Materials Reading 7Two small beads having positive charges q, = 5q and q, = q are fixed at the opposite ends of a horizontal insulating rod of length d = 2.25 m. The bead with charge q, 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? 91 92 d m
- A small plastic ball with a mass of 6.65 10-3 kg and with a charge of +0.149 µC is suspended from an insulating thread and hangs between the plates of a capacitor (see the drawing). The ball is in equilibrium, with the thread making an angle of 30.0° with respect to the vertical. The area of each plate is 0.0138 m2. What is the magnitude of the charge on each plate? COne end of a light spring with force constant k = 125 N/m is attached to a wall, and the other end to a metal block with charge qa A second block with charge qB = -3.62 µC is brought close to the first block. The spring stretches as the blocks attract each other so that at equilibrium, the blocks are separated by a distance 1.92 µC on a horizontal, frictionless table as shown in the figure. d = 11.0 cm. What is the displacement x of the spring? m | Aa 60000000000 +Three charges are located as shown in the figure, with values q1 = 3.4 × 10-16 C, q2 = -1.9 × 10-16 C, q3 = 6.25 × 10-16 C. The charges are separated by d1 = 2.4 × 10-6 m and d2 = 2.4 × 10-6 m. a. What is the force of q2 on q1 in the x direction, Fx? Give your answer in newtons, and recall k = 8.988 × 109 N m2/C2. b. What is the force of q3 on q1 in the y direction, Fy? Give your answer in newtons.
- Two stationary point charges +3.00 nCnC and +2.00 nCnC are separated by a distance of 50.0 cmcm. An electron is released from rest at a point midway between the two charges and moves along the line connecting the two charges. What is the speed of the electron when it is 10.0 cmcm from the +3.00 nCnC charge? Express your answer with the appropriate units.A small plastic ball of mass 5.86 x 10-3 kg and charge +0.178 µC is suspended from an insulating thread and hangs between the plates of a capacitor (see the drawing). The ball is in equilibrium, with the thread making an angle of 30.0° with respect to the vertical. The area of each plate is 0.01293 m². What is the magnitude of the charge on each plate? Number p Units + + 30.0⁰ + TA TA T I