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.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?Under electrostatic conditions, the excess charge on a conductor resides on its surface. Does this mean that all the conduction electrons in a conductor are on the surface?
- 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 = 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.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?
- 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?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.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)
- In free space, the electric field is given by E = Eo cosz costazFind the charge density ρv that will produce this field.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.A semi-infinite line extending from – o to 0 carries a uniform charge distribution of 100 nC/m. Find the electric field intensity at P(0, 0, 2). If a charge of -1 µCs placed at P, calculate the force acting on it.