A long, nonconducting, solid cylinder of radius 4.0 cm has a nonuniform volume charge density p that is a function of radial distance r from the cylinder axis: p = Ar. For A = 2.5 µC/m³, what is the magnitude of the electric field at r = 3.0 cm. Give your answer in N/C.
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- I I. A::A A Imssb1.mutah.edu.jo A small mass charged sphere (q= 3 µC) is attached by an insulating string to the surface of a very large conductor with a surface charge density of o = 21.1 µC. Given that the string makes an angle with the surface equal to 30 degrees, find the tension ( in N) in the string. use ɛo = 8.8542x10-12 F.m-1. String Select one: O A. 8.25 O B. 28.25 OC. 7.15 D. 14.30 E. 21.45 + + + + + +A solid insulating sphere of radius R has a volume charge density p given by p= pexp(-r/a"), where po.a >0 are both constants and r is the distance from the center of the insulator. Which of the following gives the correct expression for the electric fiekd magnitude at a distancer< R inside the insulator? A. E- exp В. Е exp fo 3 c. E = - (-)} D. E = - e(-)} exp E. E= 1-expA non-uniformly charged insulating sphere has a volume charge density p that is expressed as p= Br where B is a constant, and r is the radius from the center of the sphere. If the, the total charge of the sphere is Q and its maximum radius is R. What is the value for B? Sol. By definition, the volume charge density is expressed infinitesimally as p= where in is the infinitesimal charge and is the infinitesimal volume. so, we have P = dq/ = B so we can write this as dq = B dV But, dV = dr By substitution, we get the following dq = 4B dr Using Integration operation and evaluating its limits, the equation, leads to Q = Rearranging, we get B = 4)
- A non-uniformly charged insulating sphere has a volume charge density p that is expressed as p= Br where B is a constant, and r is the radius from the center of the sphere. If the, the total charge of the sphere is Q and its maximum radius is R. What is the value for B? Sol. By definition, the volume charge density is expressed infinitesimally as p= where in is the infinitesimal charge and is the infinitesimal volume. So, we haye p = dq/ So we can write this as dq = B dV But, dV = dr By substitution, we get the following dq = 4BT dr Using Integration operation and evaluating its limits, the equation, leads to Q = BT Rearranging, we get B = /( TA non-uniformly charged insulating sphere has a volume charge density p that is expressed as p= Br where B is a constant, and r is the radius from the center of the sphere. If the, the total charge of the sphere is Q and its maximum radius is R. What is the value for B? Sol. By definition, the volume charge density is expressed infinitesimally as p= where in is the infinitesimal charge and is the infinitesimal volume. so, we have p = dq/ So we can write this as dq = B dV %3D But, dV = drQUESTION 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 = 2
- Charge is distributed throughout a spherical volume of radius R with a density p = ar², where a is a constant (of unit C/m³, in case it matters). Determine the electric field due to the charge at points both inside and outside the sphere, following the next few steps outlined. Hint a. Determine the total amount of charge in the sphere. Hint for finding total charge Qencl = (Answer in terms of given quantities, a, R, and physical constants ke and/or Eg. Use underscore ("_") for subscripts, and spell out Greek letters.) b. What is the electric field outside the sphere? E(r> R) = c. What is the electric field inside the sphere? Hint for E within sphere #3 Question Help: Message instructor E(r < R) = Submit Question E с $ 4 R G Search or type URL % 5 T ^ MacBook Pro 6 Y & 7 U * 8 9 0 0A non-uniformly charged insulating sphere has a volume charge density p that is expressed as p= Br where B is a constant, and r is the radius from the center of the sphere. If the, the total charge of the sphere is Q and its maximum radius is R. What is the value for B? Sol. By definition, the volume charge density is expressed infinitesimally as where in is the infinitesimal charge and is the infinitesimal volume. so, we have p = dq/ so we can write this as dq = B dV But, dV = dr By substitution, we get the following dq = 4BT dr Using Integration operation and evaluating its limits, the equation, leads to Q = Rearranging, we get B = 4)Problem: An infinitely long cylindrical conductor has radius R and uniform surface charge density O. In terms of Rand O, what is the charge per unit length A for the cylinder? Answer: A = 2
- A thick insulating spherical shell of inner radius a=1.2R and outer radius b=5.5R has a uniform charge density p. b. What is the magnitude of the electric field at r=8.9 R ? Express your answer using one decimal place in units of pR €oa) Find the surface charge density σ2 of the cylindrical shell of radius R2. (Note the unit in the input box and the sign of charges.) Surface charge density σ2Give your answer up to at least three significance digits. b) Find an expression of electric field at rmm from the center where R1<r<R2. Assume the cylinder has a length L and L is very long so that electric field is uniform. Consider that the insulating material between the cylinders is air. (Hint : use Gauss's law and cylindrical Gaussian surface with radius r.) Magnitude of the electric field at r=0.76mm Give your answer up to at least three significance digits. c) Calculate absolute value of the potential difference between the wire and the cylinder. Absolute value of the potential difference Give your answer up to at least three significance digits. d) Calculate the capacitance C for this cylindrical system. Assume that the length of the cylinder is L=17cm. Capacitance C for this cylindrical system Give your…An 4.7 meter long and 0.195 diameter tube is filled with Hydrogen in the presence of a uniform electric field of 2,720x104 V/m directed from side A to side B along the tube axis. What is the surface bound charge density on surface B? Express your answer in nC/m2. Assume that the hydrogen is in mono-atomic form (not diatomic form) obeying the ideal gas law at STP. Note that STP is at 0 degrees celcius and 100,000 Pa.