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If the electric field in some region is given (in spherical coordinates)by the expression
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- A solid conducting sphere, which has a charge Q1 =84Q and radius rg = 1.5R is placed inside a very thin spherical shell of radius rp = 3.4R and charge Q2 =15Q as shown in the figure below. Q2 Tb Q1 ra Find the magnitude of the electric field at r=6.2. Express your answer using one decimal point in units 1 where k = 4περ of karrow_forwardA thick insulating spherical shell of inner radius a = 3, 13R and outer radius b = a uniform charge density p. = a b 10, 73R has What is the magnitude of the electric field at r = 14, 82R? Express your answer using two PR decimal places in units ofarrow_forwardQUESTION 1 Problem: An infinitely long cylindrical conductor has radius R and uniform surface charge density o. In terms of R and o, what is the charge per unit length A for the cylinder? Answer: A = 2arrow_forward
- Let the electric field in a certain region of space be given by E (F)= CF/ €, a² where a has dimension of length and C' is a constant. The charge density p(F) is given by (a) p=0 (b) p = 3Cla (c) p = C €, la (d) p = C/e, [H.C.U.-2013]arrow_forwardE(r) = Bzi - ax'y'j+ (6@yxy + Bóz³) k %3D where a, B, y and & are constants and r = xi+yj+zk. Find the corresponding charge density p(r).arrow_forwardProblem: An infinitely long cylindrical conductor has radius R and uniform surface charge density Ơ. In terms of R and o, what is the charge per unit length A for the cylinder? Answer: A = 2arrow_forward
- 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 rp has charge -Q. The electric field E at a radial distance r from the central axis is given by the function: E = aer/ao + B/r + bo %3D where alpha (a), beta (B), ao and bo are constants. Find an expression for its capacitance. First, let us derive the potential difference Vab between the two conductors. The potential difference is related to the electric field by: Vab = | S"Edr= - [ *Edr Calculating the antiderivative or indefinite integral, Vab = (-aage-r/ao + B + bo By definition, the capacitance C is related to the charge and potential difference by: C = Evaluating with the upper and lower limits of integration for Vab, then simplifying: C = Q/( (e-rb/ao - eralao) + B In( ) + bo ( ))arrow_forwardProblem: An infinitely long cylindrical conductor has radius R and uniform surface charge density 0. In terms of R and o, what is the charge per unit length A for the cylinder? Answer: A = 2arrow_forwardThe volumetric charge density of a cylinder of radius R is proportional to the distance to the center of the cylinder, that is, ρ = Ar when r≤R, with A being a constant. (a) Sketch the charge density for the region - 3R < r < 3R. What is the dimension of A?b) Calculate the electric field for a point outside the cylinder, r > Rc) Calculate the electric field for a point inside the cylinder, r<R.d) Sketch Exrarrow_forward
- An infinitely long cylinder in free space is concentric with the z-axis and has radius a. The net charge density p in this cylinder is given in cylindrical coordinates by, 1 a² +r² where A is a constant. (a) Show that the total charge per unit length, λ in the cylinder is λ = πA ln 2. p(r) = A- Hint: you may find the following integral useful. 1 2 J for r a) and inside the cylinder (r< a). (d) The cylinder is composed of a material in which the polarisation P is given by P = P₁² in (1 +5²) e₁₁ er, r where Po is a constant. Determine the bound charge density pb in the cylinder. Hence, or otherwise, determine a relation between A and Po such that the free charge density of in the cylinder vanishes.arrow_forwardElectric charge is distributed over the disk a2 + y < 20 so that the charge density at (x,y) is o(x, y) = 5 + x² + y² coulombs per square meter. Find the total charge on the disk.arrow_forwardPositive charge is distributed in a sphere of radius R that is centered at the origin. Inside the sphere, the electric field is Ē(r) = kr-1/4 f, where k is a positive constant. There is no charge outside the sphere. a) How is the charge distributed inside the sphere? In particular, find an equation for the charge density, p. b) Determine the electric field, E(r), for r > R (outside the sphere). c) What is the potential difference between the center of the sphere (r = 0) and the surface of the sphere (r = R)? d) What is the energy stored in this electric charge configuration?arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning