Question

A point charge is placed at the centre of a closed gaussian is spherical surface how is electric flux surface affected when the sphere is replaced by cylinder of the same or different volume

Answer 1

a.) If the surface is replaced by a cube of the same volume?
YES the flux changes || NO the flux does not change

b.) If the sphere is replaced by a cube of 1⁄4 the volume?
YES the flux changes || NO the flux does not change

c.) If the charge is moved off center in the original sphere, but remains inside? YES the flux changes || NO the flux does not change

d.) If the charge is moved outside the original sphere?
YES the flux changes || NO the flux does not change

e.) If a second charge is placed near, but still outside the original sphere? YES the flux changes || NO the flux does not change

f.) If a second charge is placed inside the Gaussian surface?
YES the flux changes || NO the flux does not change

2.) There exists an E-Field such that: Ex=ax2, Ey=0, Ez=0. A cube (side length L) is placed in this region in the following manner:

a.) What is the electric flux( ΦE ) through this cube?

b.) What charge is contained in the cube?

3.) This problem involves 2D planes of conductors. The heights and widths of the planes should be assumed to be very large compared to the distance of their separation. Note that each plane will have two surfaces, which for the purposes of this problem we will refer to as the Left (L) and Right (R) surfaces. Assume all the planes are in vacuum with permittivity ε0.

3a.) For this part, there is a single 2D plane of a charged conductor with positive surface charge density +σ. Using Gauss’ Law, derive an expression for the magnitudes of the electric fields to the left and to the right of the insulating plane at all points in space. In the figure, sketch the direction of the field on each side of the plane and the surface you used to calculate Gauss' Law

3b.) In this part, there are five 2D planes of charged conductors. They all have surface charge density σ but some are positive and some are negative. The planes are separated by non-zero, finite distances and form six distinct regions (1 – 6) to the left and right of the planes. Compute the expressions for the magnitudes of the Electric Field in each of these regions (E1 – E6). In the figure above, sketch the direction of the E-field in each of the regions.

Hint: Yes, there is a trick to this. No, it shouldn’t take pages of work