By using Gauss's Law, show that the electric field in the space between the two conductors of a coaxial cable is given by: E(r) τρι 2πει where "-p" is the linear line charge density (Coulombs / meter) defined for the inner conductor.
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- The surface charge density on a long straight metallic pipe is . What is the electric field outside and inside the pipe? Assume the pipe has a diameter of 2a.A very long, thin wile has a uniform linear charge density of 50C/m . What is the electric field at a distance 2.0 cm from the wire?Consider a uranium nucleus to be sphere of radius R=7.41015 m with a charge of 92e distributed uniformly throughout its volume. (a) is the electric force exerted on an electron when it is 3.01015 m from the center of the nucleus? (b) What is the acceleration of the electron at this point?
- Problem: 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 = 2Problem: 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 = 2An infinite cylinder of radius R has a charge density given by p(r) = ar³, where r is the perpendicular distance from the axis of the cylinder, and a is a constant. Show that the electric field for r > R given by aRT E(r) : 7€or is the same as that obtained if all the charge is concentrated in an infinitely thin wire.
- A dielectric rod with cross-section area of A and polarization of Px = ax² + b is extended from x = 0 to x = L. (a) Calculate the bound volume charge density and bound surface charge density. b) Determine the total bound charge.Consider a conductor with total charge of −12q. The conductor has a cavity, and there is a+15q charge inside the cavity. How much charge is on the outer surface of the conductor?In free space, the electric field is given by E = Eo cosz costazFind the charge density ρv that will produce this field.
- Which one(s) of the following statement(s) is(are) correct. (i) Both the Coulomb's law and the Gauss's law can be used to calculate the electric field if the charge distribution has a certain symmetry. (ii) The electric fiekl of a finitely long eylindrical wire carrying uniform volume charge density can be caleulated by using the Gauss's law. (ii) The electric field of a charged conducting spherical shell can be caleu- lated by using the Gauss's law. Select one (i) and (ii) (i) and (ii) Only (ii) Only (i) (i) and (iii)An infinitely long cylindrical conductor has radius R and uniform surface charge density. In terms of R and, what is the charge per unit length for the cylinder?A flat wire of infinite length has width W and charge density sigma. If we align the wire so that it is everywhere at y=0 and extends in x from x=d to x=d+L, then calculate the electric field at x=0. Hint: Treat the wire as an the sum of the contributions of many "long wires" where the linear charge density satisfies: lambda=sigma*L.