A 70.0-g block carrying a charge Q = 31.0 µC is connected to a spring for which k = 72.0 N / m. The block lies on a horizontal frictionless surface and is immersed in a uniform electric field of magnitude E = 4.64 ✕ 104 N / C directed as shown in the following figure. The block is released from rest when the spring is not stretched (x = 0). (a) By what maximum distance (in cm) does the block move from its initial position? (b) Determine (in cm) the rear equilibrium position of the block and the range of its motion. (Indicate the address with the sign of your answer.) (c) Using conservation of energy, find a symbolic relationship that gives the potential difference between your initial position and the point of maximum extension in terms of the spring constant k, the amplitude A, and the charge Q.

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? C

A positively charged particle of mass 50 grams and charge 10 µC is released from rest at the origin in the uniform electric field of 100 N/C  directed along the +X-axis. Determine its speed at x = 10 cm position.

A small drop of water is suspended motionless in air by a uniform electric field that is directed upward and has a magnitude of 7420 N/C. The mass of the water drop is 4.78 × 10-9 kg. How many excess electrons or protons reside on the drop

The drawing shows an electron entering the lower left side of a parallel plate capacitor and exiting at the upper right side. The initial speed of the electron is 3.13 × 106 m/s. The capacitor is 2.00 cm long, and its plates are separated by 0.150 cm. Assume that the electric field between the plates is uniform everywhere and find its magnitude. 15.30 + A + 2.00 cm Number i + + + 0.150 cm Units

A particle of charge +7.3 µC is released from rest at the point x = 79 cm on an x axis. The particle begins to move due to the presence of a charge Q that remains fixed at the origin. What is the kinetic energy of the particle at the instant it has moved 40 cm if (a)Q=+38 µC and (b)Q--38 µC? (a) Number: (b) Number Units Units

A spherical capacitor is composed of two concentric conducting spheres, one of radius a and the other of radius c (c > a). In addition, between the two conductors there is a spherical shell of dielectric material (relative permittivity/relative dielectric constant ) with inner radius b (c > b > a) and outer radius c. The charge on the inner conductor is +Q. The charge on the outer conductor is -Q. (a) Make a sketch of the situation, indicating the relevant dimensions. (b) Determine the magnitude of the electric field E at radius r for a < r < b. (c) Determine the magnitude of the electric field E at radius r for b < r < c. (d) What is the (induced) surface charge density on the inner surface of the dielectric. (e) Sketch the radial component of the electric field versus r . (f) Sketch the electrostatic potential versus r . (g)Calculate the potential difference between the conductor at r = a and that at r = c. (h) What is the capacitance of this capacitor?

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 = 15.0 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 D0D0D_0 = 2.15 cm, where there is a uniform vertical electric field with magnitude E = 7.70×104 N/C.  1) If a drop is to be deflected a distance d = 0.340 mmmm 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.