1.53 A particle with charge q=3 μC and mass 0.015 kg is tied to a non- conductive thread of length L = 17.5 cm long, which is tied at a pivot point p. The particle is on a friction-free horizontal table. At a given instant, the particle is released from rest, when the position of the thread forms an angle of 60°, with a uniform electric field of E = 350 V/m horizontally. Determine the speed of the particle when the wire and the electric field are collinear. E L=r FgE sen F=qE

A proton is located at the origin, and a second proton is located on the x-axis at x = 6.00 fm (1 fm = 10-15 m). (a) Calculate the electric potential energy associated with this configuration. (b) An alpha particle (charge = 2e, mass = 6.64 1027 kg) is now placed at (x, y) = (3.00, 3.00) fm. Calculate the electric potential energy associated with this configuration. (c) Starting with the three-particle system, find the change in electric potential energy if the alpha particle is allowed to escape to infinity while the two protons remain fixed in place. (Throughout, neglect any radiation effects.) (d) Use conservation of energy to calculate the speed of the alpha particle at infinity. (e) If the two protons are released from rest and the alpha panicle remains fixed, calculate the speed of the protons at infinity.

Four charged particles are at rest at the corners of a square (Fig. P26.14). The net charges are q1 = q2 = 2.65 C and q3 = q4 = 5.15 C. The distance between particle 1 and particle 3 is r13 = 1.75 cm. a. What is the electric potential energy of the four-particle system? b. If the particles are released from rest, what will happen to the system? In particular, what will happen to the systems kinetic energy as their separations become infinite? FIGURE P26.14 Problems 14, 15, and 16.

Four charged particles are at rest at the corners of a square (Fig. P26.14). The net charges are q1 = q2 = +2.65 C and q3 = q4 = 5.15 C. The distance between particle 1 and particle 3 is r13 = 1.75 cm. a. What is the electric potential energy of the four-particle system? b. If the particles are released from rest, what will happen to the system? In particular, what will happen to the systems kinetic energy?

An election enters a region between two large parallel plates made of aluminum separated by a distance of 2.0 cm and kept at a potential difference of 200 V. The electron enters through a small hole in the negative plate and moves toward the positive plate. At the time the electron is near the negative plate, its speed is 4.0103 m/s. Assume the electric field between the plates to be uniform, and find the speed of electron at (a) 0.10 cm, (b) 0.50 cm, (c) 1.0 cm, and (d) 1.5 cm from the negative plate, and (e) immediately before it hits the positive plate.

A charge of 81 pC is distributed on an isolated spherical conductor that has a radius of 4 cm . Point A is 0.9 cm from the center of the conductor and point B is 5 cm from the center of the conductor. Determine the electric potential difference VA – VB. The value of Coulomb’s constant is 8.98755 × 10° N · m²/C². Answer in units of V.

A small ball with charge q = 12.8 μC and mass m = 0.065 kg is suspended from the ceiling by a string of length L = 2 m and is initially at rest. A uniform horizontal electric field E of magnitude 500 V/m is applied to the ball-string system. The ball then begins to move. Ignore air resistance. a)Suppose point B is the highest point the ball can reach. Take θ as the angle of the string with the vertical direction at point B. Enter an expression for the change of gravitational potential energy ΔUg from point A to point B in terms of the symbols given.  b) Enter an expression for the change of the electrical potential energy ΔUe from point A to point B in terms of the symbols given.

The ink drops have a mass mmm = 1.00×10−11 kg each and leave the nozzle and travel horizontally toward the paper at velocity v = 22.0 m/s. The drops pass through a charging unit that gives each drop a positive charge q by causing it to lose some electrons. The drops then pass between parallel deflecting plates of length D0 = 1.65 cmcm , where there is a uniform vertical electric field with magnitude E = 7.55×104 N/C If a drop is to be deflected a distance d = 0.250 mm by the time it reaches the end of the deflection plate, what magnitude of charge q must be given to the drop? Assume that the density of the ink drop is 1000 kg/m3, and ignore the effects of gravity.

A proton which charge is 1.602x10^-19 C moves in a straight line from point  A to B inside a linear accelerator, a total distance d=0.40 m. The electric field is uniform along this line, with magnitude E=2.5x10^7 V/m or N/C in the direction from A to B. Determine tie potential difference.

A constant electric field of 20.0 N/C points along the positive x-direction. An electron, initially at rest, moves a distance of 0.500 m in this space. How fast is the electron moving after its 0.500 m journey?