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A solid cylindrical conductor of radius a is surrounded by a concentric cylindrical shell of inner radius b. The solid cylinder and the shell carry charges
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- Two solid spheres, both of radius 5 cm, carry identical total charges of 2 C. Sphere A is a good conductor. Sphere B is an insulator, and its charge is distributed uniformly throughout its volume. (i) How do the magnitudes of the electric fields they separately create at a radial distance of 6 cm compare? (a) EA EB = 0 (b) EA EB 0 (c) EA = EB 0 (d) 0 EA EB (e) 0 = EA EB (ii) How do the magnitudes of the electric fields they separately create at radius 4 cm compare? Choose from the same possibilities as in part (i).arrow_forwardFigure (a) shows a nonconducting rod with a uniformly distributed charge +Q. The rod forms a 10/25 of circle with radius R and produces an electric field of magnitude Earc at its center of curvature P. If the arc is collapsed to a point at distance R from P (see Figure (b)), by what factor is the magnitude of the electric field at P multiplied? (a) +Q Number R i P MI Units +Q |—R— P This ansarrow_forwardSuppose 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 rh has charge -Q. The electric field E at a radial distancer from the central axis is given by the function: E = ae-r/ao + B/r + bo 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 = Edr = - Edr Calculating the antiderivative or indefinite integral, Vab = (-aaoe-r/ao + B + bo By definition, the capacitance C is related to the charge and potential difference by: C= Q I Vabarrow_forward
- A cylinder has a length L and radius R. It has a non-uniform charge distribution p such that p = por? for rR Find the electric field both inside and outside the cylinder.arrow_forwardSuppose 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 rh has charge -Q. The electric field E at a radial distance r from the central axis is given by the function: E = ae-r/ao + B/r + bo 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 = Edr = - Edr Calculating the antiderivative or indefinite integral, Vab = (-aager/ao + B + bo By definition, the capacitance Cis 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 - eTalao) + B In( ) + bo ( ))arrow_forwardA rod of length l = 1.0 m has a charge per unit length λ = 5(x – a) C/m, a < x < l.Calculate the electric field at a point P that is located along the long axis of the rod and a distance 20.99 cmfrom one end.arrow_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 = ae-r/ao + B/r + bo 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: ['´e Vob = Edr= - Edr Calculating the antiderivative or indefinite integral, Vab = (-aaoe¯r7ao + 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 / ( (erb/ao - eralao) + B In( ) + bo ( ))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_forwardin 4 decimalsarrow_forward
- A long straight conducting cable (cylindrical in shape like a long straight wire) has a radius of a = 0.5 cm. At a perpendicular distance of r = 3 cm from the center of the cable, the electric field has a magnitude of 7 N/C, and is directed radially inward. How much charge per unit length (in C/m) exists on the cable?arrow_forward(a) A spherical metal conductor (Q = 7.5C) is placed r = 0.9 m from an identical conductor with a different charge (q = 13.6 C). The two conductors are brought into contact and separated. What is the electric charge on either sphere after they have come into contact? Answer in SI units. (b) What is the magnitude of the initial electrical field (conductors in their initial configuration) at the midpoint between the two conductors? Answer in SI units and multiply your answer by 10^-11.arrow_forwardA spherical charge distribution of ρ = ρ0 [1-r^2 / b^2] is in the region 0≤r≤b. This load distribution is concentrically surrounded by a spherical shell of inner radius R1 (R1> b) and outer radius R2. Find E in regions r≤b, b≤ r ≤ R1 , R1≤ r ≤ R2, r≥R2?arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
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