An infinite plan slab of thickness (2d) carries a "frozen-in"uniform polarization (P). Caluculate the potential of the electricfield V(x) induced by this polarized slab as a function of thedistance x from the center.

description( x-coordinate is normal to the surface of the slab. x=0is in the center of the slab. x=d is one surface and x=-d is theother surface.

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An infinitely long rod of radius R carries a uniform volumecharge density rho (rho > 0).

(a) Show how to use Gauss' Law to prove that the
electric field inside this rod points radially
outward and has magnitude

E = (rho*r)/(2*epsilon_0).

(b) Find the potential difference between a initial
radial position r_i and a final radial position
r_f; i.e. find an expression for the potential
at r_i subtracted from the potential at r_f.

(c) Choose potential equal zero at the central axis
of the rod and find the potential as a function
of r inside the rod (i.e. for r < R). Make a
graph of your resulting potential function (plot
V versus r).

(d) Instead of the case in (c), choose potential equal
zero at the surface of the rod (i.e. at r=R) and
find the potential as a function of r inside the
rod (i.e. for r < R). Again make a graph of your
resulting potential function (plot V versus r).

Please explain your strategy and include any labels ordiagrams.

An infinitely long rod of radius R carries a uniform volume chargedensity rho (rho > 0).

(a) Show how to use Gauss' Law to prove that the
electric field inside this rod points radially
outward and has magnitude

E = (rho*r)/(2*epsilon_0).

(b) Find the potential difference between a initial
radial position r_i and a final radial position
r_f; i.e. find an expression for the potential
at r_i subtracted from the potential at r_f.

(c) Choose potential equal zero at the central axis
of the rod and find the potential as a function
of r inside the rod (i.e. for r < R). Make a
graph of your resulting potential function (plot
V versus r).

(d) Instead of the case in (c), choose potential equal
zero at the surface of the rod (i.e. at r=R) and
find the potential as a function of r inside the
rod (i.e. for r < R). Again make a graph of your
resulting potential function (plot V versus r).

Please explain your strategy and include any labels ordiagrams.

An infiinitely long solid conducting cylindrical shell ofradius a = 4.4 cm and negligible thickness is positioned with itssymmetry axis along the z-axis as shown. The shell is charged,having a linear charge density ?inner = -0.36 ÂµC/m. Concentric withthe shell is another cylindrical conducting shell of inner radius b= 17 cm, and outer radius c = 19 cm. This conducting shell has alinear charge density ? outer = 0.36ÂµC/m.

1) What is Ex(P), the x-component of theelectric field at point P, located a distance d = 9.4 cm from theorigin along the x-axis as shown?

2) What is V(c) â V(a), the potential differencebetween the the two cylindrical shells?

3) What is C, the capacitance of a one meter length ofthis system of conductors?

The magnitudes of the charge densities on the inner and outershells are now changed (keeping ?inner = -?outer) so that theresulting potential difference doubles (Vca,new =2Vca,initial).

What is ?outer,new ?

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