Applying Gauss’ law Cylindrical Symmetry
The drum of the photocopying machine in Exercise has a length of 42 cm and a diameter of 12 cm What is the total charge on the drum (b) The manufacturer wishes to produce a desktop version of the machine This require reducing the size of the drum to a length of 28 cm and a diameter of 8.0 cm. The electric field at the drum surface must remain unchanged. What must be the charge on this new drum An infinite line of charge produces a field of 4.5 x 104 N/C at a distance of 2.0 m. Calculate the linear charge densite shows a section of a long. them-walled metal tube of radius R. with a charge per unit length A on its surface. Deriv c expressions
for E in terms of the distance r from the tube axis considering both (a) r > Hand (b) r < R. Plot your results for the range r = 0 to r = 5.0 em.
assuming that A = 2.0 X JO ” C/m and R = 3.0 Col. (HI/II: Use C) cylindrical Gaussian surfaces. convivial with the mew I tub A very long conducing C)- cylindrical rod of length L a charge +q is surrounded by a conducting cylindrical shell charge Use to (a) the electric field at points outside the
conducting shell (11) the distribution of charge on the shell and (c) the electric field in the region between the shell and rod A long straight wire has fixed negative charge with a linear charge density of magnitude The wire ;5 to be enclosed by a thin. nonconducting cylinder of outside radius
coaxial with the wire The cylinder is to has e positive charge on its outside surface” ith a surface charge density a such that the net external electric field is zero. Calculate the required Two long charged concentric cylinders have radii of 3.0 and 6.0 Col. The charge per unit length is 5.0 x 10 6 C/m on the inner cylinder and -7.0 X 10 6 C/m on the outer cylinder. Find the
electric field at (a) r = 4.0 earn and (b) r = 8.0 er here r is the radial distance from the common central axis A long nonconducting. solid cylinder of radius ~.O cm has a nonuniform volume charge density p that is a function of the radial distance I from the axis of the cylinder. as given b with What is the magnitude of the electric field at a radial distant e of (a) 3.0 cm and (b) 5.0 ern from the axis of the cylinder shows a Geiger counter a device used to detect ionizing radiation (radiation that causes ionization of atoms) The counter consists of a thin positively charged central wire surrounded by a concentric. circular conducting cylinder with an equal negative charge Thus a strong radial electric field is set up inside the cylinder The cylinder contains a low-pressure inert gas When a panic of radiation enters the device through the cylinder. all. it ionizes a few of the gas toms. The resulting free electrons label e) are drawn 10 the positive” ire. However the field is so intense that. between collisions with other g toms. the free electrons gain energy sufficient to ionize these atoms also. More free electrons arc thereby c.eared. and the process is repeated until the electron reach the wire. The resulting “avalanche’ of electron> is collected the generating a signal that is used to record the passage of the Original panic of radiation Suppose that the radius of the central the radius of the cylinder and the length of the tube 16 em. If the electric field at the cylinder inner wall is 2.9 X 10” “Ie. what is the total positive charge on
the central article A charge of slumlord linear density 2.0 ne/m is distributed along a long. them, nonconducting rod. The rod 1\ coaxial long. hollow. conducting c~Lind (inner radius = 5.0. outer radii = 10 . The net charge on the conductor is zero. (a) What Is the magnitude of the electric field 15 from the a~i, of ) tinder? What is the surface charge density on (b) the inner surface (c) the outer surface of the conductor 25P Charge is distributed uniformly throughout the volume of an infinitely long c~ linder of radius R. Show that. at a distance r from the cylinder.
here p is the volume charge density (b) Write an expression for E “hen R.