Consider a quarter-circular, very thin, curved rod with a uniform linear charge density, λ, and a radius, r. Derive an equation for the magnitude of the electric field at the point, P, at the center curvature of the rod, as shown in the figure below
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Consider a quarter-circular, very thin, curved rod with a uniform linear charge density, λ, and a
radius, r. Derive an equation for the magnitude of the electric field at the point, P, at the center
curvature of the rod, as shown in the figure below. Write the final answer in terms of λ and r, and simplify your answer as much as possible.
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- Charge is distributed throughout a spherical shell of inner radius ₁ and outer radius r2 with a volume density given by p= Por1/r, where po is a constant. Following the next few steps outlined, determine the electric field due to this charge as a function of r, the distance from the center of the shell. Hint a. Let's start from outside-in. For a spherical Gaussian surface of radius r>r2, how much charge is enclosed inside this Gaussian surface? Hint for finding total charge Qencl (Answer in terms of given quantities, po, r1, 72, and physical constants ke and/or Eo. Use underscore ("_") for subscripts, and spell out Greek letters.) b. What is the electric field as a function of r for distances greater than r₂? Finish the application of Gauss's Law to find the electric field as a function of distance. E(r> r₂) c. Now let's work on the "mantle" layer, r₁The charge per unit length on the thin rod shown below is 1. 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 = 1 dx. Then find the net field by integrating dE over the length of the rod. Use the following as necessary: L, a, 1, and ɛn: Enter the magnitude. Assume that 1 is positive.) E =Charge is distributed throughout a spherical shell of inner radius r₁ and outer radius r2 with a volume density given by p= Pori/r, where po is a constant. Following the next few steps outlined, determine the electric field due to this charge as a function of r, the distance from the center of the shell. Hint a. Let's start from outside-in. For a spherical Gaussian surface of radius r > r2, how much charge is enclosed inside this Gaussian surface? Hint for finding total charge Because the charge density is a function of r, rather than being able to multiply the charge density by the volume, row you need to integrate over the volume. The amount of charge in a spherical shell of radius r and thickness dr is p(r). 4tr²dr; integrate this from r = r₁ to r = r₂ to obtain the total amount of charge. Qencl= (Answer in terms of given quantities, po, 71, 72, and physical constants ke and/or Eo. Use underscore ("") for subscripts, and spell out Greek letters.) b. What is the electric field as a…In the diagram below, there is areal charge density o in the region bounded by green. (I don't know enough about Word to actually fill the region.) The inner arc has radius of curvature R₁, and the outer arc has radius R₂. (a) Consider a thin piece of the shape lying in a band between r and r+dr, as shown in the figure. How much charge lies in this band? (b) Integrate your result from previous problem to find the electric field at the origin in terms of R1, R2, σ, and B. y В -ß r+dr XUse Gauss's Law in to solve problems 1 to 3, showing and justifying your steps and using related conceptual diagrams and mathematical formula as needed. (1) Find the Electric Field outside an infinitely long slab with uniform charge density sigma. (2): Find the Electric Field (a) outside and (b) inside a non-conducting solid sphere with uniformly distributed charge Q. (3) Find the Electric Field outside an infinitely long rod with uniform charge density lambda.Calculate the x-component of the electric field produced by the charge distribution Q at points on the positive x-axis. Positive charge Q is distributed uniformly along the positive y-axis between y = 0 and y = a. Anegative point charge -g lies on the positive x-axis, a distance z from the origin (the figure (Figure 1). Express your answer in terms of some or all of the variables Q. z, y, a, and constant k. ? Ex = a Calculate the y-component of the electric field produced by the charge di: Express your answer in terms of some or all of the variables Q. z. y. u. au vUIIaLas K- O I9 Ey = Calculate the x-component of the force that the charge distribution Q exerts on q. Express your answer in terms of some or all of the variables Q. z, y. a, and constant k. ΑΣΦ ? F; = Calculate the y-component of the force that the charge distrībution Q exerts on g. Express your answer in terms of some or all of the variables Q. z. y. a. and constant k VO JAZO O I9 ? F; =Show that the following expression for the electric field a distance z along the central axis of a thin ring of continuous positive charge is correct. Derive the expression based upon the geometry shown in the diagram below. Let q-total charge of the ring, R=radius of ring. Be sure to state the magnitude and direction of the electric field at the point P.The figure below shows a section of a very thin, very long, straight rod with a uniform charge per unit length of λ. Point O is a perpendicular distance d from the rod. A spherical gaussian surface is centered at point O and has a radius R. (Use any variable or symbol stated above along with the following as necessary: ε0.) A)What is the electric flux through the spherical surface if R < d? B)What is the electric flux through the spherical surface if R > d?= Adx. Then find the net field by integrating dE over the length of the rod. Use the following as The charge per unit length on the thin rod shown below is 2. 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 . necessary: L, a, 2, and ɛn. Enter the magnitude. Assume that A is positive.) L A 1 E = 4ne L+A aWhat is the strength in (N/C) of the electric field at the position indicated by the dot in the diagram above? The charge on the points labeled A and A* is +1.57 nC. The x distance is 8.99 cm. What is the angle (in degrees) of the electric field at the position indicated by the dot in the diagram above? Take the point to be the origin and the angle is measured counterclockwise from the horizontal axis away from A.The figure below shows a section of a very thin, very long, straight rod with a uniform charge per unit length of 1. Point O is a perpendicular distance d from the rod. A spherical gaussian surface is centered at point O and has a radius R. (Use any variable or symbol stated above along with the following as necessary: £0.) R (a) What is the electric flux through the spherical surface if R d? ⓇE=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 RSEE MORE QUESTIONS