For the purpose of calculating the electric field strength by means of Gauss’s law, determine whether approximate cylindrical symmetry holds in each of the following situations.
Part (a) We have a 3.6-m long copper rod of radius 1 cm, carrying a charge of 1.5 nC distributed uniformly along the rod’s length. We want to calculate the electric field strength at a point 4.9 cm from the rod near its center.
TRUE FALSE
Part (b) We have a 8.9-cm long copper rod of radius 1 cm, carrying a charge of 1.5 nC distributed uniformly along the rod’s length. We want to calculate the electric field strength at a point 4.9 cm from rod near its center.
TRUE FALSE
Part (c) A 1.9-m long wooden rod is glued end-to-end to a 1.9-m long plastic rod, both of radius 1 cm. The combined rod is then painted with an electrically charged paint so that it is covered with a uniform charge density, giving it total charge of 1.5 nC. We want to calculate the electric field strength at a point 4.9 cm from the rod near its center.
TRUE FALSE
Part (d) For the same charged rod as in part (c) we want to calculate the electric field strength at a point 8.9 m from each end of the rod.
TRUE FALSE

a) In this case, length of the copper rod is 3.6 m which is much larger than the distance 4.9 cm to the point at which electric field is to be determined. Therefore, yes, cylindrical symmetry holds.

b) In this case, length of the copper rod is 8.9 cm which is of the same order of magnitudes the distance 4.9 cm to the point at which electric field is to be determined. Therefore, no, cylindrical symmetry does not hold.

c) In this case, length of the copper rod is 3.8 m which is much larger than the distance 4.9 cm to the point at which electric field is to be determined. Therefore, yes, cylindrical symmetry holds.

d) In this case, length of the copper rod is 3.6 m which is of the same order of magnitudes the distance 4.9 cm to the point at which electric field is to be determined. Therefore, no, cylindrical symmetry does not hold.