Considera flat, circular washer lying in the xy plane, with the center at the origin of the coordinate system. The washer has an inner radius and an outer radius . The surface of the washer isuniformly charged with a surface charge density (>0). A point p is situated at a distance from the origin along the axis of symmetry of the washer (see the figure below).XOOOE =E =What is the electric field at point P due to the washer?Ood11==[kwry]{√ [ (₁² + 4²) ²/² = (b ² + 1²) 3/7²] ²2ę3/2E =aE =ZdadPbodaਕਰਦਾEb√b²+d²1√b²+d²²o[√/a²+d²ad1SIA2ea01√b²+d²

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A solid disk of radius R = 11 cm lies in the y-z plane with the center at the origin. The disk carries a uniformly distributed total charge Q = 45 μC. A point P is located on the positive half of the x-axis a distance 24 cm from the origin. Refer to the diagram, where the y- and z-axes lie in the plane of the screen and the x-axis points out of the screen. a. Enter an expression for the surface charge density σ in terms of the total charge and radius of the disk. σ = b. Consider a thin ring of the disk of width dr located a distance r from the center. Enter an equation for the infinitesimal charge in this thin ring in terms of Q, R, r, and dr. dQ = c. Calculate the electric potential at P, in kilovolts. V = d. Calculate the magnitude of the electric field at the point P in units of meganewtons per coulomb. E =
Question 6 := Homework. Unanswered Multiple Plates -- Two infinite, uniformly charged plates have the same magnitude of surface charge density O. They are orientated in the illustration looking down the planes. Please note that is a positive value. Place your target in a region (inside a blue circle) of net electric field that points to the RIGHT. To do this, you will have to add two constant electric field vectors produced by the Then select the region where the net field points to the RIGHT. Figure [6.24]. planes for each region. 00 -0 Undo Delete selected Remove All o O Targets placed: 0/1 You can place up to 1 targets
A small plastic ball of mass m = 1.50 g is suspended by a string of length L = 17.0 cm in a uniform electric field, as shown in the figure below. If the ball is in equilibrium when the string makes a ? = 17.0° angle with the vertical as indicated, what is the net charge on the ball? A ball of mass m is attached to a string of length L and suspended from the ceiling. The string makes an acute angle ? with the normal line from the ceiling, such that the string and ball are displaced to the right of the normal line. To the right of the string and ball, five parallel, evenly-spaced, identical arrows point to the right. The arrows are vertically stacked and labeled with E = 1.00 ✕ 103 N/C. To the left of the string and ball, x y-coordinate axes demonstrate that the +x-axis points to the right and the +y-axis points up.
Four different configurations show charge distributions and closed Gaussian surfaces. Assume that the surface normals are directed outward for each closed surface. If a charge appears to be located within a Gaussian surface, then it is, as opposed to being in the foreground or the background. The charges have the following values: q1= -22.6 nC q2= +32.7 nC q3= +3.58 nC q4= -3.29 nC q5= +5.41 nC Part (a) What is the total electric flux, in newtons squared meters per coulomb, through the closed surface shown in drawing (a) of the figure? Part (b) What is the total electric flux, in newtons squared meters per coulomb, through the closed surface shown in drawing (b) of the figure? Part (c) What is the total electric flux, in newtons squared meters per coulomb, through the closed surface shown in drawing (c) of the figure? Part (d) Drawing (d) of the figure shows a portion of an infinite conductng plane viewed edge-on. The Gaussian surface is a "Gaussian pillbox" whose sides are…
Shown in the figure below is a hollow disk of charge. The disk carries a charge density ? and has an inner radius R1 and an outer radius R2. You are to calculate the magnitude of the field at the point P which is a distance z above the plane of the disk. Determine the area element, dA = Determine the charge element, dQ = Determine the distance, s = Determine the so-called, cos(?) = Determine the integrand, ∬ Determine the lower bound of the ? integral: Determine the upper bound of the ? integral: Determine the lower bound of the r integral: Determine the upper bound of the r integral: Determine the final result of the integration: NOTE: Please use k in your answers. Please do not use ?0.
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
A cube is located with one corner at the origin of an x, y, z coordinate system. One of the cube's faces lies in the x, y plane, another in the y, z plane, and another in the x, z plane. In other words, the cube is in the first octant of the coordinate system. The edges of the cube are 2.21 m long. A uniform electric field is parallel to the x, y plane and points in the direction of the +y axis. The magnitude of the field is 8970 N/C. What is the electric flux through the cubical surface? Number i Units
An infinitely long rod lies along the x-axis and carries a uniform linear charge density λ = 5 μC/m. A hollow cone segment of height H = 27 cm lies concentric with the x-axis. The end around the origin has a radius R1 = 8 cm and the far end has a radius R2 = 16 cm. Refer to the figure. a. Consider the conic surface to be sliced vertically into an infinite number of rings, each of radius r and infinitesimal thickness dx. Enter an expression for the electric flux differential through one of these infinitesimal rings in terms of λ, x, and the Coulomb constant k. b. Integrate the electric flux over the length of the cone to find an expression for the total flux through the curved part of the cone (not including the top and bottom) in terms of λ, H, and the Coulomb constant k. Enter the expression you find. c. Calculate the electric flux, in N•m2/C, through the circular end of the cone at x = 0. d. Calculate the electric flux, in N•m2/C, through the circular end of the cone at x = H. e.…
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 Z 2 = ( ₁ = √√²²+R² 1 and use superposition.) - magnitude of the electric field at point Pat z = 2.01 cm? (Hint: See equation E = X X X Number i 0.365 Units N/C or V/m
S: x 0' R 4x Note: Figure not drawn to scale. The figure above shows a thin, circular nonconducting sheet of positive charge uniformly distributed over its area. The radius of the sheet is R. Point O is at the center of the sheet. Point S is a distance x from the center of the sheet, and point T is a distance 4x from the center of the sheet. Assume R>>x if the magnitude of the electric field at point T is ET, which of the following best represents the magnitude of the electric field at point S?
-2Q + 2Q a P -x direction X A semicircle of radius a is in the second and third quadrants, with the center of the curvature at the origin. Positive charge +2Q is distributed uniformly around the bottom half of the semicircle, and negative charge -2Q is distributed uniformly around the top half of the semicircle as shown in the figure. What is the direction of the net electric field at the origin produced by this distribution of charge?