a) Check that the results of Exs. 2.5 and 2.6, and Prob. 2.11, are consistent with Eq. 2...

a) Check that the results of Exs. 2.5 and 2.6, and Prob. 2.11, are consistent with Eq. 2.33.

(b) Use Gauss’s law to find the field inside and outside a long hollow cylindrical tube, which carries a uniform surface charge σ. Check that your result is consistent with Eq. 2.33.

(c) Check that the result of Ex. 2.8 is consistent with boundary conditions 2.34 and 2.36.

Reference example 2.5

An infinite plane carries a uniform surface charge σ. Find its electric field.

Reference example 2.6

Two infinite parallel planes carry equal but opposite uniform charge densities ±σ (Fig. 2.23). Find the field in each of the three regions: (i) to the left of both, (ii) between them, (iii) to the right of both.

Reference prob 2.11

Use Gauss’s law to find the electric field inside and outside a spherical shell of radius R that carries a uniform surface charge density σ. Compare your answer to Prob. 2.7.

Reference Prob. 2.7

Reference example 2.8

Find the potential of a uniformly charged spherical shell of radius R (Fig. 2.33).