A thin rod of length l and uniform charge per unit length a lies along the axis as shown in the figure. (a) Show that the electric field at P, a distance d from the rod along its perpendicular bisector, has no x component and is given by 1 sin 0 E = 2ke d (b) What If? Using your result to part (a), show that the field of a rod of infinite length is = 24, E = 2ke d

A thin rod of length l and uniform charge per unit length a lies along the axis as shown in the figure. (a) Show that the electric field at P, a distance d from the rod along its perpendicular bisector, has no x component and is given by 1 sin 0 E = 2ke d (b) What If? Using your result to part (a), show that the field of a rod of infinite length is = 24, E = 2ke d

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter19: Electric Forces And Electric Fields

Section: Chapter Questions

Problem 18P

See similar textbooks

Similar questions

Suppose the conducting spherical shell of Figure 15.29 carries a charge of 3.00 nC and that a charge of -2.00 nC is at the center of the sphere. If a = 2.00 m and b = 2.40 m. find the electric field at (a) r = 1.50 m, (b) r = 2.20 m, and (c) r = 2.50 m. (d) What is the charge distribution on the sphere?
Two infinite, nonconducting sheets of charge are parallel to each other as shown in Figure P19.73. The sheet on the left has a uniform surface charge density , and the one on the right hits a uniform charge density . Calculate the electric field at points (a) to the left of, (b) in between, and (c) to the right of the two sheets. (d) What If? Find the electric fields in all three regions if both sheets have positive uniform surface charge densities of value .
Recall that in the example of a uniform charged sphere, p0=Q/(43R3). Rewrite the answers in terms of the total charge Q on the sphere.
Determine if approximate cylindrical symmetry holds for the following situations. State why or why not. (a) A 300-cm long copper rod of radius 1 cm is charged with +500 nC of charge and we seek electric field at a point 5 cm from the center of the rod. (b) A 10-cm long copper of radius 1 cm is charged with +500 nC of charge and we seek electric field at a point 5 cm from the center of the rod. (c) A 150-cm wooden rod is glued to a 150-cm plastic rod to make a 300 cm long rod, which is then painted with a charged paint so that one obtains a uniform charge density. The radius of each rod is 1 cm, and we seek an electric field at a point that is 4 cm from the center of the rod. (d) Same rod as (c), but we seek electric field at a point that is 500 cm from the center of the rod.
A long, straight wire is surrounded by a hollow metal cylinder whose axis coincides with that of the wire. The wire has a charge per unit length of , and the cylinder has a net charge per unit length of 2. From this information, use Gausss law to find (a) the charge per unit length on the inner surface of the cylinder, (b) the charge per unit length on the outer surface of the cylinder, and (c) the electric field outside the cylinder a distance r from the axis.
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.
What is the force on the charge q at the lower-right-hand comer of the square shown here?
What is the magnitude of the electric field due to a charged particle at its exact location (r = 0)?
A positive charge q = 7.81 μC is spread uniformly along a thin nonconducting rod of lengthL = 15.4 cm. What are the (a) magnitude and (b) direction (relative to the positive directionof the x axis) of the electric field produced at point P, at distance R = 6.00 cm from the rod along itsperpendicular bisector?
The field due to two parallel plates, the left with a negative surface charge density of −6.0 C/m2 whilethe sheet on the right has a positive surface charge density of +9.0 C/m2is given below. Suppose the plates were spaced 0.0020 m apart. We found that, using Gauss’s law that, independent of this distance, • In I the net field points to the left and has magnitude |Enet| = 1.69 × 1011 N/C.• In region II, between the plates, the field has magnitude 8.47×1011 N/C and points to the left• In III it points to the right and has magnitude |Enet| = 1.69 × 1011 N/C.
Show that the maximum magnitude Emax of the electric field along the axis of a uniformly charged ring occurs at x = a/√2 (as shown) and has the value Q/(6√3π∈0a2).
As shown in Figure, a particle of charge +Q produces an electric field of magnitude Epart at point P, atdistance R from the particle. As in figure b, that same amount of charge is spread uniformly along a circulararc that has radius R and subtends an angle ?. The charge on the arc produces an electric field of magnitudeEarc at its center of curvature P. For what value of ? does Earc = 0.50 Epart ?