A long conducting cylindrical rod of length L with a total charge +q and radius a is surrounded by a long coaxial conducting cylindrical shell of the same length with an inner radius b and an outer radius c containing a total charge of -4q as shown in the figure on the right. The length Lis much larger than a, b, and c. (a) What is the magnitude and direction of the electric field outside the conductors? (b) How much charge are there on the inner wall of the shell? (c) Calculate electric potential difference between the conductors. (d) Obtain an expression for the capacitance C of the conductor in terms of the parameters (a, b, c, and L) of the two conductor -4q system.

A long conducting cylindrical rod of length L with a total charge +q and radius a is surrounded by a long coaxial conducting cylindrical shell of the same length with an inner radius b and an outer radius c containing a total charge of -4q as shown in the figure on the right. The length Lis much larger than a, b, and c. (a) What is the magnitude and direction of the electric field outside the conductors? (b) How much charge are there on the inner wall of the shell? (c) Calculate electric potential difference between the conductors. (d) Obtain an expression for the capacitance C of the conductor in terms of the parameters (a, b, c, and L) of the two conductor -4q system.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

You have the same line of charge in the previous problem (with +6.00 nC of charge on it). But now you are measuring the electric field 1.5 m above the center of the rod – see image below. Predict the electric field at Point P in this diagram. Make sure to include a direction with your answer.
A thin rod is bent into a half circle of radius R and centered on the y-axis so that it lies flat in the xy-plane as indicated in the diagram. This glass rod is rubbed all over with silk so that the rod has a total positive charge Q uniformly distributed over the length of the bent rod. Answer the following questions to determine the net electric field at an observation location A located on the positive z-axis a distance d from the origin. (See pic 1 for the following questions) A. Consider an infinitesimal piece of the glass rod located at an angle θ\thetaθ from the positive x-axis. Determine the relative position vector that points from this piece of the rod to the observation location. B. Derive an expression for the electric field dE⃗ of the infinitesimal piece dQ located at angle θ and integrate over the charge distribution to determine the net electric field E⃗ at the observation location. Your answer should only contain the given variables (R, Q, d) and known…
In Figure (a) below, a particle of charge +Q produces an electric field of magnitude Epart at point P, at distance R from the particle. In Figure (b), that same amount of charge is spread uniformly along a circular arc that has radius R and subtends an angle 8. The charge on the arc produces an electric field of magnitude Earc at its center of curvature P. For what value of 0 (in º) does Earc = 0.75Epart? (Hint: You will probably resort to a graphical solution.) +Q |▬▬▬R—-|| Number i P (a) AR +Q}/0/2/ (b) Units ° (degree:
State what is meant by electric field strength at a point in space. How is its direction defined? Given that the magnitude field strength, E, at a distance r from a point charge Q is given by the formula: E = 4πεο r2 calculate the magnitude of the electric field at a point which is 10 cm from a positive 24 µC charge. Use E = = 9 × 10° m/F. 4πεο
LC-3 A line of positive charge lies along the x axis extending from x-0 to x-L. The total charge Q on the lines is evenly distributed along the length L. Find the net electric field at point P, which is a distance 'a' from the origin on the x axis as shown in the figure to the right. Follow the steps in the "Procedure for Applying - Coulomb's Law" that is in the "Worksheets" handed out the first day of class. Give your answer in terms of K, Q, a, L and any other constants needed. y a P X
Use Gauss's law to find the electric field at the field point in the following case. The distance between the field point and the surface of the conductor is d. A semi-infinitely large conductor with surface charge density o. Field point d х Conductor
We have calculated the electric field due to a uniformly charged disk of radius R, along its axis. Note that the final result does not contain the integration variable r: R. Q/A 2€0 Edisk (x² +R*)* Edisk perpendicular to the center of the disk Uniform Q over area A (A=RR²) Show that at a perpendicular distance R from the center of a uniformly negatively charged disk of CA and is directed toward the disk: Q/A radius R, the electric field is 0.3- 2€0 4.4.1b
Use the figure below. There is a point charge of 6.20 microCoulombs inside a spherical conducting shell with inner radius a=3.10 m and outer radius b=3.35 m. There is a total charge of 15.50 microCoulombs on the spherical shell. What is the electric field at r=2.85 m from the point charge (ie inside the shell)? (Treat + as away from the point charge and negative as toward the point charge. Answer in N/C).
A uniformly charged rod of length L and total charge Q lies along the x axis as shown in in the figure below. (Use the following as necessary: Q, L, d, and ke.) Ey= P d Ⓡ (a) Find the components of the electric field at the point P on the y axis a distance d from the origin. Ex= Eyz (b) What are the approximate values of the field components when d >> L? Ex L Explain why you would expect these results. This answer has not been graded yet. Need Help? Read It
Problem 1: Part (a) Express the magnitude of the electric field between the two plates, E, in terms of the charge q on one plate, its area A, and ε0. E = ______ Part (b) Express the electric flux ΦE, in terms of q and ε0. ΦE = ______ Part (c) Express the derivative of ΦE with respect of time t in terms of I and ε0. dΦE/dt = ______ Part (d) What is the displacement current which is passing through the capacitor in amps? ID = ______ A
Problems 4-5 refer to the following diagram and situation. A point charge (with charge Q) at the end of an insulating cord is observed to be in equilibrium in a uniform horizontal electric field of when the pendulum's angle with the vertical is 0 = 38.6°, is as shown in the Figure. The electric field is to the right and the strength of the electric field is 9500 N/C. The mass of the point charge is m = 0.0200 kg and the acceleration due to gravity is 9.8 m/sec². Problem 4: What is the tension on the cord? a. 0.251 N Problem 5: What is the charge Q? a. (1.65 x 10-5)C E b. 0.451 N b. (3.65 x 10-5)C 0 Q m c. 0.651 N C. (5.65 x 10-5) C d. 0.851 N d. (7.65 x 10-5)C
A non-conducting rod of length with a uniform charge density λ and a total charge is lying along the x-axis, as illustrated in Figure. point P, located at a distance y off the axis of the rod. Compute the electric field at a y P 8: x