2. (a) A -12 nC charge and a 5 nC charge are located on the x-axis at x=-1 cm and x=5 cm respectively. i.At what distance (in cm) directly above the 5nC charge is the electric potential equal to zero? 08.97 01.07 05.80 04.13 02.75 02.39 ii.What is the electric field (in N/C) at this location (given as a magnitude and the proper polar angle)? Magnitude 01.76e+05 047100 O1.14e+05 O21100 081100 054100 Angle 0172 0242 0374 O99.7 O44.7 O115 iii.How far to the left of the -12nC charge does the electric potential equal -27V? 02.37 07.74 05.01 O2.07 O0.926 O3.56 iv. What is the magnitude (in N/C) of the electric field at this location? 011.6 017.3 04.51 O10.1 O37.7 O24.4 (b) Two very small metal point-like spheres with masses 6 g and 10 g are tied together by a 4 cm long massless string and are at rest on a frictionless surface. Each is charged to 5 UC. i.What is the energy (in J) of this system? 02.19 04.89 05.63 08.44 O11.9 O18.3 ii.What is the tension (in N) in the string? 0297 0211 0458 0122 054.8 0141 iii.The string is cut. What is the speed (in m/s) of each sphere when they are far apart? (HINT: You will need to use TWO conservation laws here. One of them is Energy Conservation, think back to Physics I for the other). Speed of m1 O34.2 O13.4 0112 O29.8 O72.2 O51.3 Speed of m2 O20.5 043.3 067.0 08.01 O30.8 O17.9

The potential in a region between x = 0 and x = 6.00 m V = a + bx, where a = 10.0 V and b = -7.00 V/m. Determine (a) the potential at x = 0, 3.00 m, and 6.00 m and (b) the magnitude and direction of the electric field at x = 0, 3.00 m. and 6.00 m.

Two 5.00-nC charged particles are in a uniform electric field with a magnitude of 625 N/C. Each of the particles is moved from point A to point B along two different paths, labeled in Figure P26.65. a. Given the dimensions in the figure, what is the change in the electric potential experienced by the particle that is moved along path 1 (black)? b. What is the change in the electric potential experienced by the particle that is moved along path 2 (red)? c. Is there a path between the points A and B for which the change in the electric potential is different from your answers to parts (a) and (b)? Explain. FIGURE P26.65 Problems 65, 66, and 67.

Given two particles with 2.00-C charges as shown in Figure P20.9 and a particle with charge q = 1.28 1018 C at the origin, (a) what is the net force exerted by the two 2.00-C charges on the test charge q? (b) What is the electric field at the origin due to the two 2.00-C particles? (c) What is the electric potential at the origin due to the two 2.00-C particles? Figure P20.9

The naturally occurring charge on the ground on a fine day out in the open country is -1.00nC/m2. (a) What is the electric field relative to ground at a height of 3.00 m? (b) Calculate the electric potential at this height. (C) Sketch electric field and equipotential lines for this scenario.

A uniform electric field of magnitude 325 V/m is directed in the negative y direction in Figure P20.1. The coordinates of point are (0.200, 0.300) m, and those of point are (0.400, 0.500) m. Calculate the electric potential difference using the dashed-line path. Figure P20.1

A proton is released from rest at the origin in a uniform electric field in the positive x direction with magnitude 850 N/C. What is the change in the electric potential energy of the proton-field system when the proton travels to x = 2.50 m? (a) 3.40 X I0-l6J (b) -3.40 X 10-16J (c) 2.50 X 10-6J (d) -2.50 X 10-6J (e) -1.60 X 10-19J

Figure P24.22 represents a graph of the electric potential in a region of space versus position x, where the electric field is parallel to the x axis. Draw a graph of the x component of the electric field versus x in this region. Figure P24.22

A long thin wire is used in laser printers to charge the photoreceptor before exposure to light. This is done by applying a large potential difference between the wire and the photoreceptor. a. Use Equation 26.23, V(r)=20lnRr to determine a relationship between the electric potential V and the magnitude of the electric field E at a distance r from the center of the wire of radius R (r R). b. Determine the electric potential at a distance of 2.0 mm from the surface of a wire of radius R = 0.80 mm that will produce an electric field of 1.8 106 V/m at that point.

A filament running along the x axis from the origin to x = 80.0 cm carries electric charge with uniform density. At the point P with coordinates (x = 80.0 cm, y = 80.0 cm), this filament creates electric potential 100 V. Now we add another filament along the y axis, running from the origin to y = 80.0 cm. carrying the same amount of charge with the same uniform density. At the same point P, is the electric potential created by the pair of filaments (a) greater than 200 V, (b) 200 V, (c) 100 V, (d) between 0 and 200 V, or (e) 0?