Positive charge Q is distributed uniformly alongthe x-axis from x = 0 to x = a. A positive point charge q is locatedat x = a + r (see figure on the right).(a) Find the electric field due to the charge Q at the location of(at x = a + r).(b) Find the electric force that Q exerts on q. Show that for theI Qqandlimiting case r >> a, the force reduces to F%!a.4Tɛ, r²explain why you achieve this result.

Given: Positive charge Q Distributed uniformly along the x-axis from x = 0 to x = a. A positive…

Answered: Positive charge Q is distributed…

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter5: Electric Charges And Fields

Section: Chapter Questions

Problem 83P: The charge per unit length on the thin rod shown below is . What is the electric field at the point...

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Two particles with charges q1 and q2 are separated by a distance d, and each exerts an electric force on the other with magnitude FE. a. In terms of these quantities, what separation distance would cause the magnitude of the electric force to be halved? b. In terms of these quantities, what separation distance would cause the magnitude of the electric force to be doubled?
Point charges q1=50C and q2=25C are placed 1.0 m apart. (a) What is the electric field at a point midway between them? (b) What is the force on a charge q3=20C situated there?
The charge per unit length on the thin rod shown below is . What is the electric field at the point P? (Hint: Solve this problem by first considering the electric field dE at P due to a small segment dx of the rod, which contains charge dq=dx . Then find the net field by integrating dE over the length of the rod.)
In this exercise, you practice electric field lines. Make sure you represent both the magnitude and direction of the electric field adequately. Note that the number of lines into or out of charges is proportional to the charges. (a) Draw the electric field lines map for two charges +20C and 20C situated 5 cm from each other. (b) Draw the electric field lines map for two charges +20C and +20C situated 5 cm from each other. (c) Draw the electric field lines map for two charges +20C and 30C situated 5 cm from each other.
The charge per unit length on the thin rod shown below is λ.λ. What is the electric force on the point charge q? Solve this problem by first considering the electric force dF⃗ dF→ on q due to a small segment dxdx of the rod, which contains charge λdx.λdx. Then, find the net force by integrating dF⃗ dF→ over the length of the rod.
In Figure 1, an insulating rod is bent into a semicircle of radius R. A charge -Q is uniformly distributed along its top half (for 0 < theta < pi/2) while a charge +Q is uniformly distributed along its bottom half (for -pi/2<theta< 0). Find the lectrostatic force in unit vector notation, acting on an electron with charge -e which is located at the origin O.
The charge per unit length on the thin rod shownbelow is λ . What is the electric field at the point P? (Hint:Solve this problem by first considering the electric fieldd E→ at P due to a small segment dx of the rod, whichcontains charge dq = λdx . Then find the net field byintegrating d E→ over the length of the rod.)
The charge per unit length on the thin rod shown below is λ . What is the electric field at the point P? (Hint: Solve this problem by first considering the electric field dE at P due to a small segment dx of the rod, which contains charge dq = λdx . Then find the net field by integrating dE over the length of the rod.)
Consider the symmetrically arranged charges in the figure, in which Qa=Qb=−1.95 μC and Qc=Qd=+1.95 μC. Determine the direction of the electric field at the location of charge q . Calculate the magnitude of the electric field E at the location of q given that the square is 6.75 cm on a side.
Consider three charges arranged in a triangleas shown. What is the net electric force on the chargeat the origin? The value of the Coulombconstant is 8.99 × 10^9 N · m^22/C^2.Answer in units of N. What is the direction of this force (as an anglebetween −180◦and +180◦ measured from thepositive x-axis, with counterclockwise positive)?Answer in units of ◦ What is the magnitude of the net electric fieldat the position of the charge at the origin?Answer in units of N/C. What is the direction of the net electric field(as an angle between −180◦and +180◦ measured from the positive x-axis, with counterclockwise positive).Answer in units of ◦.
For the following charge arrangement with q1 = -q2 = q3 and a = 4b, in what quadrant will be the vector that represents the net force on q1 due to the other two charges?
Repeat your calculations for the preceding problem (shown below),given that the charge is distributed uniformly over thesurface of a spherical conductor of radius 10.0 cm. A charge of −30 μC is distributed uniformlythroughout a spherical volume of radius 10.0 cm.Determine the electric field due to this charge at a distanceof (a) 2.0 cm, (b) 5.0 cm, and (c) 20.0 cm from the centerof the sphere.

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