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Charge is distributed throughout a very long cylindrical volume of radius R such that the charge density increases with the distance r from the central axis of the cylinder according to
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- Cylindrical shell of inner radius R₁ = 1.85 R and outer radius R₂ = 2.39 R is filled uniformly with charge density p. A point charge Q = 5.3q is located at point A a distance 7.97 R from the center of the cylinder. What is the magnitude of the force acts on the cylinder by the point charge. Express your answer in terms of qpR/e using two decimal places. Р R1 R₂ A Qarrow_forwardIn free space, a linear charge density > is on the z axis. Get the electric force over a unit charge "q" located at P (1, 2, 3) m if the linear charge density is in -4 m < z < 4m = 2μC m Give the answer in unit vectors terms.arrow_forwardA uniformly charged rod of length L lies along the x-axis with its right end at the origin. The rod has a total charge of Q. A point P is located on the x-axis a distance a to the right of the origin. Write an equation for the electric field dE at point P due to the thin slice of the rod dx. Give the answer is terms of the variables Q, L, x, a, dx, and coulombs constant k. Integrate the electric field contributions from each slice over the length of the rod to write an equation for the net electric field E at point P. Calculate the magnitude of the electric field E in kilonewtons per coulomb (kN/C) at point P due to the charged rod if L = 2.2m, Q = 8.5 μC and a = 1.1m.arrow_forward
- Problems 11-13 refer to the following situation. A nonuniform, but spherically symmetric, distribution of charge has a charge density p(r) given as follows: Problem 11: What is the constant po? Q πR³ a. Po and R are positive constants. The total charge of the distribution is Q. Problem 12: What is the E-field for r R? 1 Q b. 4περ 12 a. p(r) = {Po (7) . 20 πR³ 1 Qr² 4περ R4 1 QR 4περ 13 C. C. r R C. 30 πR³ 1 Qr³ 4περ R5 QR² 1 4περ 14 d. d. d. 4Q πR³ 1 Qr4 4πεο R6 QR³ 1 Απο 15arrow_forwardA charge is distributed over a spherical body of radius R so that the density of the volumetric charge at any point of this space follows the relationship p = kr where k is constant and r is after the point from the center of this spherical space. Find the value of E at any point where is rarrow_forwardA very thin charged rod of length L lies on the z-axis (x=0, y=0) centered on the origin (z=0) and extending in the range – L/2 L/2, by integrating the formula [convert dq to the specific case of the linear charge density] 1 V (†) dq(7') 4πεο (b) Calculate the electric field vector E (0,0, z) at the same point as in part (a) by using the definition of the electric field in terms of the potential.arrow_forward(a) Figure (a) shows a nonconducting rod of length L = 5.80 cm and uniform linear charge density λ = +4.87 pC/m. Take V = 0 at infinity. What is Vat point P at distance d= 7.50 cm along the rod's perpendicular bisector? (b) Figure (b) shows an identical rod except that one half is now negatively charged. Both halves have a linear charge density of magnitude 4.87 pC/m. With V=0 at infinity, what is Vat P? L/2 (a) -L/2 L/21/2- (b)arrow_forwardAn infinite line of charge produces a field of magnitude E=7x10* N/C 8- at distance 3 m. Find the linear charge density.arrow_forwardAn 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_forwardAn infinite sheet of charge, oriented perpendicular to the x-axis, passes through x = 3 μC/m2. 0. It has a surface charge density o1 = A thick, infinite conducting slab, also oriented perpendicular to the x-axis, occupies the region between a = 2.6 cm and b = 4.6 cm. The conducting slab has a net charge per unit area of 02 = 78 µC/m2. (Recall that the surface charge densities oa and oh on the slab surfaces at a and b, respectively, sum to equal the net charge per unit area: oa + ob = 02.) 1) What is Ex(P), the value of the x-component of the electric field at point P, located a distance 7.8 cm from the infinite sheet of charge? N/C Submit 2) What is Ey(P), the value of the y-component of the electric field at point P, located a distance 7.8 cm from the infinite sheet of charge? N/C Submit + 3) What is Ex(R), the value of the x-component of the electric field at point R, located a distance 1.3 cm from the infinite sheet of charge? N/C Submit 4) What is Ey(R), the value of the…arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
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