Answer Happy

Options for direction: outward, inward, no direction
A very long, very thin straight line has a uniform charge per unit length of 1, where x > 0. It is surrounded by a long, cylindrical, insulating rubber shell, which has an inner radius a and outer radius b. The line lies along the central axis of the cylindrical shell. The cylindrical shell has a uniform volume charge density, where p > 0. (Both the line and the shell are long enough to approximate them as infinitely long.) Find the electric field in the following regions by choosing a gaussian cylinder of radius r and length L. (Use any variable or symbol stated above along with the following as necessary: £n-) (a) r<a 22 magnitude E = How much charge is enclosed by the gaussian cylinder? How is the enclosed charge related to the charge per unit length? What is the direction of the electric field? What is the area of the gaussian cylindrical surface? no directionX What is the sign of the enclosed charge? direction (b) a <r<b magnitude E 22 2 + pal,2-02) How much charge is enclosed by the gaussian cylinder? What volume of cylindrical shell is enclosed? How does the volume relate to the charge density of the shell? Is the line charge still enclosed? What is the direction of the electric field? What is the area of the gaussian cylindrical surface? no direction X What is the sign of the enclosed charge? direction (c) r>D 24 2 + pal ,2- ) magnitude E = How much charge is enclosed by the gaussian cylinder? What volume of cylindrical shell is enclosed? How does the volume relate to the charge density of the shell? Is the line charge still enclosed? What is the direction of the electric field? What is the area of the cylindrical surface? no direction X What is the sign of the enclosed charge? direction (d) What If? Suppose we have the same situation as described above, where again > 0, but now p can be any value. For what value of p will there be zero electric field for r> b? px 32-02) Can you use the result of part (c) to solve for p when E = 0?