A point charge gives rise to an electric field with magnitude 1 N/C at a distance of 2 m. If the distance is increased to 4 m, then what will be the new magnitude of the electric field? N/C

(a) Find the magnitude and direction of the electric field at the position of the 2.00 C charge in Figure P13.13. (b) How would the electric field at that point be affected if the charge there were doubled? Would the magnitude of the electric force be affected?

(a) Find the electric field at x = 5.00 cm in Figure 18.52 (a), given that q = 1.00 C. (b) at what position between 3.00 and 8.00 cm is the total electric field the same as that for ? 2q alone? (c) Can the electric field be zero anywhere between 0.00 and 8.00 cm? (d) At very large positive or negative values of x, the electric field approaches zero in both (a) and (b). In which does it most rapidly approach zero and why? (e) At what position to the light of 11.0 cm is the total electric field zero, other than at infinity? (Hint: A graphing calculator can yield considerable insight in this problem.)

(a) What magnitude point charge creates a 10,000 N/C electric field at a distance of 0.250 m? (b) How large is the field at 10.0 m?

The electric field at a point on the perpendicular bisector of a charged rod was calculated as the first example of a continuous charge distribution, resulting in Equation 24.15:E=kQy12+y2j a. Find an expression for the electric field when the rod is infinitely long. b. An infinitely long rod with uniform linear charge density also contains an infinite amount of charge. Explain why this still produces an electric field near the rod that is finite.

A charge of q = 2.00 109 G is spread evenly on a thin metal disk of radius 0.200 m. (a) Calculate the charge density on the disk. (b) Find the magnitude of the electric field just above the center of the disk, neglecting edge effects and assuming a uniform distribution of charge.

A thin, square, conducting plate 50.0 cm on a side lies in the xy plane. A total charge of 4.00 108 C is placed on the plate. Find (a) the charge density on each face of the plate, (b) the electric field just above the plate, and (c) the electric field just below the plate. You may assume the charge density is uniform.

Two particles, each with charge 52.0 nC, are located on the y axis at y = 25.0 cm and y = 25.0 cm. (a) Find the vector electric field at a point on the x axis as a function of x. (b) Find the field at x = 36.0 cm. (c) At what location is the field 1.00ikN/C? You may need a computer to solve this equation. (d) At what location is the field 16.0ikN/C?

a. Figure 24.22A shows a rod of length L and radius R with excess positive charge Q. The excess charge is uniformly distributed over the entire outside surface of the rod. Write an expression for the surface charge density . Write an expression in terms of for the amount of charge dq contained in a small segment of the rod of length dx. b. Figure 24.22B shows a very narrow rod of length L with excess positive charge Q. The rod is so narrow compared to its length that its radius is negligible and the rod is essentially one-dimensional. The excess charge is uniformly distributed over the length of the rod. Write an expression for the linear charge density . Write an expression in terms of for the amount of charge dq contained in a small segment of the rod of length dx. Compare your answers with those for part (a). Explain the similarities and differences.

A coaxial cable consists of a long, straight filament surrounded by a long, coaxial, cylindrical conducting shell. Assume charge Q is on the filament, zero net charge is on the shell, and the electric field is E1i at a particular point P midway between the filament and the inner surface of the shell. Next, you place the cable into a uniform external field Ei. What is the x component of the electric field at P then? (a) 0 (b) between 0 and E1 (c) E1 (d) between 0 ant E1 (e) E1