1- A metal ball with a mass of 7. *10-6 kg and a charge of +6 mC has a kinetic energy of 2. *108 J. It is traveling directly at an infinite plane of charge with a charge distribution of +5 C/m2. If it is currently 1 m away from the plane of charge, how close will it come to the plane before stopping? Ans:- 0.882 m
2- A proton gun fires a proton from midway between two plates, A and B, which are separated by a distance of 83.0 cm; the proton initially moves at a speed of 135.0 km/s toward plate B. Plate A is kept at zero potential, and plate B at a potential of 400.0 V.
(a) Will the proton reach plate B?
(b) If not, where will it turn around? (If the proton reaches plate B, enter 0.830 m, the distance between the plates.)
(c) With what speed will it hit plate A? (If the proton reaches plate B, enter 0.) Ans:- No. 0.612 m, 2.38e+05 m/s.
3- Consider a dipole with charge q and separation d. What is the potential a distance x from the center of this dipole at an angle θ with respect to the dipole axis, as shown in the figure? (Do not assume that x » d. Use any variable or symbol stated above along with the following as necessary: k.)
4- Consider an electron in the ground state of the hydrogen atom, separated from the proton by a distance of 0.0529 nm.
(a) Viewing the electron as a satellite orbiting the proton in the electrostatic potential, calculate the speed of the electron in its orbit.
(b) Calculate an effective escape speed for the electron.
(c) Calculate the energy of an electron having this speed. Using this energy, determine the energy that must be given to the electron to ionize the hydrogen atom. Ans:- 2.19e+06 m/s; 3.10e+06 m/s; 4.36e-18 J; 13.6 eV
5- An electric field varies in space according to this equation: E→ = E0xe-x→. (a) For what value of x does the electric field have its largest value, xmax? (Use the following as necessary: E0.) (b) What is the potential difference between the points at x = 0 and x = xmax? (State an expression for the difference V(xmax) - V(0). Use the following as necessary: E0.) Ans:- 1.
6- An infinite plane of charge has a uniform charge distribution of +5 nC/m2 and is located in the yz-plane at x = 0. A +24 nC fixed point charge is located at x = +1 m. (a) Find the electric potential V(x) on the x-axis from 0 < x < +1 m. (Use the following as necessary: x, k, σ for the surface charge distribution, and q and x0 for the charge and position of the point charge, respectively. Do not substitute numerical values; use variables only.) (b) At what position(s) on the x-axis between x = 0 and x = +1 m is the electric potential a minimum? (Enter your answers from smallest to largest starting with the first answer blank. Enter NONE in any remaining answer blanks.)
7- The electric field, E→(r→), and the electric potential, V(r →), are calculated from the charge distribution, ρ(r →), by integrating Coulomb's Law and then the electric field. In the other direction, the field and the charge distribution are determined from the potential by suitably differentiating. Suppose the electric potential in a large region of space is given by V(r) = V0 exp (-r2/a2), where
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V0 and a are constants and r = √
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x2 + y2 + z2
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is the distance from the origin. (a) Find the electric field E→(r→) in this region. (Use the following as necessary: V0, r, a, and ε0.) (b) Determine the charge density ρ(r →) in this region, which gives rise to the potential and field. (Use the following as necessary: V0, r, a, and ε0.) (c) Find the total charge in this region. (Use the following as necessary: V0, r, a, and ε0.) (d) Roughly sketch the charge distribution that could give rise to such an electric field.
8- Two metal balls of mass m1 = 6 g (diameter = 6 mm) and m2 = 7 g (diameter = 7 mm) have positive charges of q1 = 1 nC and q2 = 8 nC, respectively. A force holds them in place so that their centers are separated by 8 mm. What will their velocities be after the force is removed and a large distance separates them? (Enter the magnitudes of the velocities.) Ans:- 0.0402 m/s; 0.0344 m/s
9- A charge of 0.520 nC is placed at x = 0. Another charge of 0.140 nC is placed at x1 = 10.9 cm on the x-axis. (a) What is the combined electrostatic potential of these two charges at x = 20.1 cm, also on the x-axis? (b) At which point(s) on the x-axis does this potential have a (local) minimum? (Enter your answers from smallest to largest starting with the first answer blank. Enter NONE in any remaining answer blanks. If you need to use ∞or -∞, enter INFINITY or -INFINITY, respectively.) Ans:- 36.9 V; -Infinity; 7.18 cm; Infinity.