Figure 20.35 shows a thin, uniformly charged disk of radius R . Imagine the disk divided into rings of varying radii r , as suggested in the figure, (a) Show that the area of such a ring is very nearly 2 πrdr . (b) If the disk carries surface charge density σ use the result of part (a) to write an expression for the charge d on an infinitesimal ring, (c) Use the result of (b) along with the result of Example 20.6 to write the infinitesimal electric field dE of this ring at a point on the disk axis, taken to be the positive x -axis. (d) Integrate over all such rings to show that the net electric field on the axis has magnitude E = 2 π k σ ( 1 − x x 2 + R 2 ) FIGURE 20.35 Problem 73
Figure 20.35 shows a thin, uniformly charged disk of radius R . Imagine the disk divided into rings of varying radii r , as suggested in the figure, (a) Show that the area of such a ring is very nearly 2 πrdr . (b) If the disk carries surface charge density σ use the result of part (a) to write an expression for the charge d on an infinitesimal ring, (c) Use the result of (b) along with the result of Example 20.6 to write the infinitesimal electric field dE of this ring at a point on the disk axis, taken to be the positive x -axis. (d) Integrate over all such rings to show that the net electric field on the axis has magnitude E = 2 π k σ ( 1 − x x 2 + R 2 ) FIGURE 20.35 Problem 73
Figure 20.35 shows a thin, uniformly charged disk of radius R. Imagine the disk divided into rings of varying radii r, as suggested in the figure, (a) Show that the area of such a ring is very nearly 2πrdr. (b) If the disk carries surface charge density σ use the result of part (a) to write an expression for the charge d on an infinitesimal ring, (c) Use the result of (b) along with the result of Example 20.6 to write the infinitesimal electric field dE of this ring at a point on the disk axis, taken to be the positive x-axis. (d) Integrate over all such rings to show that the net electric field on the axis has magnitude
Consider a thin rod 1 meter in length that carries a non-uniform charge density lamda = .005 mC/m2 x + .001 mc/m where x is the position of a point on the rod relative to an origin placed at one end. How much charge is on the rod? Answer in mC.
If a human nerve cell has a net charge of -8.65 pC, what are the magnitude and direction (inward or outward) of the net flux through the cell boundary? What is the charge density passing through the cell? Assume that the portion of the cell in question is spherical.
In this problem, a very long metallic rod with a uniform circular cross section of radius 0.35 mm has a constant charge per unit length of 1.5x10^-8 C/m.
A) Determine the electric field at a distance 0.20 mm from the longitudinal axis of the rod. (Possible answer: 0, 1.3 x 10^6 N/C, 1.8 x 10^6 N/C, 6.7 x 10^5 N/C, 7.7 x 10^5 N/C)
B) Determine the electric field at a distance 0.50 mm from the longitudinal axis of the rod. (Possible answer: 0, 1.8 x 10^6 N/C, 7.7 x 10^5 N/C, 5.4 x 10^5 N/C, 3.2 x 10^5 N/C)
Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
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