Using the method of integration, what is the electric field of a uniformly charged thin circular plate (with radius R and total charge Q) at xo distance from its center? (Consider that the surface of the plate lies in the yz plane) Solution A perfect approach to this is to first obtain the E-field produced by an infinitesimal charge component of the charge Q. There will be several approaches to do this, but the most familiar to us is to obtain a very small shape that could easily represent our circular plane. That shape would be a ring. So for a ring whose charge is q, we recall that the electric field it produces at distance x0 is given by E = (1/ )(x0q)/( 242) Since, the actual ring (whose charge is dq) we will be dealing with is an infinitesimal part of the circular plane, then, its infinitesimal electric field contribution is expressed as = (1/ )(x0 2. We wish to obtain the complete electric field contribution from the above equation, so we integrate it from 0 to R to obtain E = (x0/ 24 Evaluating the integral will lead us to Qxo 1 1 E = 4 tE OR? Xo (x3 + R²) /2

Using the method of integration, what is the electric field of a uniformly charged thin circular plate (with radius R and total charge Q) at xo distance from its center? (Consider that the surface of the plate lies in the yz plane) Solution A perfect approach to this is to first obtain the E-field produced by an infinitesimal charge component of the charge Q. There will be several approaches to do this, but the most familiar to us is to obtain a very small shape that could easily represent our circular plane. That shape would be a ring. So for a ring whose charge is q, we recall that the electric field it produces at distance x0 is given by E = (1/ )(x0q)/( 242) Since, the actual ring (whose charge is dq) we will be dealing with is an infinitesimal part of the circular plane, then, its infinitesimal electric field contribution is expressed as = (1/ )(x0 2. We wish to obtain the complete electric field contribution from the above equation, so we integrate it from 0 to R to obtain E = (x0/ 24 Evaluating the integral will lead us to Qxo 1 1 E = 4 tE OR? Xo (x3 + R²) /2

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

A 2D annulus (thick ring) has an inner radius Ri and outer radius Ro, and charge Q non-uniformlydistributed over its surface. The 2D charge density varies with radius r by η(r)=Cr 4 for Ri ≤ r ≤ Roand η=0 for all other r. C is a constant. Answer the following in terms of the variables given above. Note: Gauss' Law will not be useful here.a) Find an expression for C such that the total charge of the annulus is Q. Include the SI units for C next to your answer.Do the units make sense?b) Draw a clear picture and use it to set up the integral to calculate the E-field at a point on the axis of the annulus (this axis is perpendicular to the plane of the annulus) a distance z from the center of the annulus. *** You must complete all the steps short of computing the integral (i.e. your eventual answer must be an integral with only ONE variable of integration and all other variables constant.) Show that your answer has the correct SI units for the electric field.
Consider an infinitesimal segment located at an angular position θ on the semicircle, measured from the lower right corner of the semicircle at x=a, y=0. (Thus θ=π2 at x=0, y=a and θ=π at x=−a, y=0.) What are the x- and y- components of the electric field at point P (dEx and dEy) produced by just this segment? Express your answers separated by a comma in terms of some, all, or none of the variables Q, a, θ, dθ, and the constants k and π.
A positively charged disk of radius R and total charge Qdisk lies in the xz plane, centered on the y axis (see figure below). Also centered on the y axis is a charged ring with the same radius as the disk and total charge Qring: The ring is a distance d above the disk. Determine the electric field at the point P on the y axis, where P is above the ring a distance y from the origin. (Use any variable or symbol stated above along with the following as necessary: k.) magnitude E = direction ---Select--- y P R
Suppose a capacitor consists of two coaxial thin cylindrical conductors. The inner cylinder of radius ra has a charge of +Q, while the outer cylinder of radius rb has charge -Q. The electric field E at a radial distance r from the central axis is given by the function:.... pls fill in the blanks
An infinitely large horizontal plane carries a uniform surface charge density = -0.368 nC/m². What is the electric field strength in the region above the plane [Select] ? A proton is traveling in this field with initial speed vo = 1.00 × 105 m/s at 0 = 45° angle with respect to the plane, as shown in the figure below Use the coordinate system in the figure and neglect the effect of gravity. How high can the proton go [Select] ? If the zero potential is at the origin level, i.e., y = 0 level, what is the potential energy [Select] and kinetic energy [Select] of the proton when it is at a height of 31 = 0.500 m? What is the proton's kinetic energy at height y2 = 2.00 m [Select] y Vo
A disk with radius R and uniform positive charge density o lies horizontally on a tabletop. A small plastic sphere with mass M and positive charge hovers motionless above the center of the disk, suspended by the Coulomb repulsion due to the charged disk. At what height h does the sphere hover? Express your answer in terms of the dimensionless constant v = 20 Mg/ (Qo). Express your answer in terms of some or all of the variables R and v. h = R- 1-v √(2-v)v Submit Part C h = Previous Answers Correct If M = 300 g, Q = 1.0 μC, R = 6.0 cm, and o = 10 nC/cm², what is h? Express your answer with the appropriate units. μᾶ Value 2 Units Submit Previous Answers Request Answer ? <
Assume a uniformly charged ring of radius R and charge Q produces an electric field E at a point Pon its axis, at distance x away from the center of the ring as in Figure a. Now the same charge Q is spread uniformly over the circular area the ring encloses, forming a flat disk of charge with the same radius as in Figure a. How does the field Eick produced by the disk at P compare with the field produced by the ring at the same point? O O Ek Ering O impossible to determine
An insulating sphere of radius a has a non-uniform volume charge density p = 4 where A is a constant and r is the spherical radial coordinate. This insulating sphere is surrounded by a concentric conducting spherical shell of inner and outer radii b and e, respectively (b>a) as shown in the figure. What are the induced surface charge densities on the inner (oinner) and outer (đouter) surfaces of the condueting shell? Select one: Aa Aa Oouter = Oinner = Aa dinner = Aa Oouter = - O'inner = -47Aa², 47 Aa? Oouter = 47 Aa 4 Aa Oinner = Jouter = b2 Ab Ac Oouter = Oinner = a² °
A long cylinder of charge q has a radius a. The charge density within its volume, p, is uniform (Figure). Describe the form of the electric field generated by the cylinder. Find the electric field strength at a distance r from the axis of the cylinder in the regions (i) r > a and (ii) 0 <r<a.If a non-relativistic electron moves in a circle at a constant distance R from the axis of the cylinder, where R > a, find an expression for its speed.
The classic Millikan oil drop experiment was the first to obtain an accurate measurement of the charge on an electron. In it, oil drops were suspended against the gravitational force by a vertical electric field. 1a. Given the oil drop to be 0.99 μm in radius and have a density of 910 kg/m3: Find the weight of the drop. 1b.If the drop has a single excess electron, find the electric field strength needed to balance its weight. This is not and will not be graded
In the figure a small circular hole of radius R = 1.55 cm has been cut in the middle of an infinite, flat, nonconducting surface that has a uniform charge density o = 6.33 pC/m². A z axis, with its origin at the hole's center, is perpendicular to the surface. What is the and use superposition.) O magnitude of the electric field at point Pat z = 2.01 cm? (Hint: See equation E = 280 Number Y X k X i X X X XX X Units < Z √z² + R²
a loaded thin rod is bent into a semicircle of radius as shown in the figure. Charge density at a point on the rod, o the angle between the position vector of the point and the vertical c R λ = Acos(θ) : It is bound by the os expression. At the center of the semicircle (point O) what is the electric field?