A very thin rod carrying linear charge density A lies in the ay plane making angle 1/4 with the x axis as shown in the figure. The x coordinates of the left and the right ends of the rod are a and b, respectively. Find the electric potential at the origin (point O), sin(7/4) = cos(T/4) = (k is the Coulomb's constant.). y T/4 x=a x=b Select one: kA In(1+ v2ª + b, a +b, |kA In(1+ª+°,

A very thin rod carrying linear charge density A lies in the ay plane making angle 1/4 with the x axis as shown in the figure. The x coordinates of the left and the right ends of the rod are a and b, respectively. Find the electric potential at the origin (point O), sin(7/4) = cos(T/4) = (k is the Coulomb's constant.). y T/4 x=a x=b Select one: kA In(1+ v2ª + b, a +b, |kA In(1+ª+°,

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)...

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Two concentric spherical conductive shells of radii 5 cm and 10 cm are charged with 6 µC and 1 µC, respectively. What is the electric potential at r=0, r=7.5cm, and r=15cm? V1= Enter a number. ix V, V2= V, V2= V.
In class, we considered the problem of a point charge q outside a grounded, conducting sphere of radius R. Assuming that the sphere was centered at the origin, we employed the ‘method of images’ to find the electrostatic potential as V (r > R) = q − qR/a ,|⃗r − azˆ| |⃗r − (R2/a)zˆ| where a > 0 is the position of the charge q on the z-axis. Consider the analogous problem where the charge q is now placed inside a hollow, grounded, conducting sphere of inner radius R, and q is at the position a < R on the z-axis. a) Find the electrostatic potential V (r < R) inside the sphere. b) Find the induced surface-charge density σ on the sphere. c) Find the magnitude and direction of the force F⃗ acting on the charge q. d) Determine the electrostatic potential V (r < R) if the sphere is instead kept at a constant potential V0. e) Determine the electrostatic potential V (r < R) when a total charge Q is put on the sphere.
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Ra1 +9 -9 Rea Consider two concentric spherical conductors, separated by an isolating material with (absolute) permittivity e. The two conductors have radius R1 and R2, they are put on a potential V and V2, which leads to a charge +q and –q sitting on them, respectively. By the problem's spherical symmetry, we see that the charge on each conductor is distributed uniformly, and that, in spherical coordinates, the electric field between the two conductors is of the form E(r) = -E(r) er. Determine the capacity C using the following steps: 1. Use Gauss's Law in integral form, with N a ball of radius r (R2 < r < R1), to find an expression for E(r) in terms of q. 2. Calculate AV = Vị – V2 using the formula - E•dr Δν and with C the black line segment indicated on the drawing (parallel with e,). 3. The capacity now follows from C = q/AV.
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The electric field due to a very long straight and uniformly charged wire is given by the following expression: E = ", where E is in N/C and r is the radial distance 2.0 from the wire (in meters). The radius of the wire is R = 0.005 m. a. Determine the magnitude (absolute value) of the electric potential difference between two points at the radial distances from the wire: r, = 0.20 m and r, = 0.40 m. b. Set up an integral that would allow you to determine the energy stored in the electric field produced by the charged wire. It is not necessary to evaluate the integral.
A thin circular disc of radius a has a total charge Q uniformly distributed over it. It lies in the x - y plane, centered on the origin. The charge density on the disc is p(F) = e ng² 8(2') for x2 + y2 ≤a² and 0 elsewhere. Calculate (a) the electrostatic potential and (b) the electric field at a general point z on the positive z axis.