For the indicated region, use Gauss’s Law to determine the magnitude of the electric field as a function of r the distance from the point charge. This requires drawing a picture, sketching the electric field, choosing a gaussian surface, calculating the charge enclosed by the surface and solving for the magnitude of the electric field.

**Please answer four questions down below and give detailed calculated steps. Thank you very much! Provide as many details as possible please. I also attached all the information you will need to answer all four questions down below.**

Xercises For Exercises 1-3, consider the system described in Example 1. For the indicated region, use Gauss\’s Law to determine the magnitude of the electric field as a function of r the distance from the point charge. This requires drawing a picture, sketching the electric field, choosing a gaussian surface, calculating the charge enclosed by the surface and solving for the magnitude of the electric field 1. The region outside of the conductor, r b 2. The region within the conducting material, a r b. You know the answer to this one is zero, but show that GausS\’s Law gives that result. 3. The region inside the conducting shell, r a 4. Consider the conducting cylinder in Example 2. Show that at points outside the conductor and very close to the surface, the formula E gives the strength of the electric field

### Solution

1)

for r > b :

considering a concentric sphere of radius r (r > b) as Gaussian surface

using Gauss Law,

total flux through surface = Qinside / e0

E . A = Qinside /e0

Qinside = +Q + (-3Q) = -2Q (minus sign means field will be radially towards centre)

E ( 4 pi r^2 ) = 2Q / e0

E = Q / (2 pi e0 r^2 )

direction radially towards centre

2). a< r < b

there is charge +Q at the centre and ████████ ███ █ ██████████████████ ██████████ ██████ ████████████ █████████████████ ████ ████████

█████████████████████ █████████ ██████ █████ ██ ███████████ ██████ █████ ██████████ ████ ███ ███ ██████████ ████████████████

(█████████████ ████████████ █████████ ████ █████████████ █████ █████████████████████)

██████ ██████ ██████████████████ █████████████ ████████ █████████ ██ (█ &███; █ &█████; ███)

██████ = ███ ██ = █

███████████ ██████ = ██

███ = █

████

██ &████; ███

█████ = ██

██ (███ ████ ██^██ ) = ███ ██ ███

██ = ███ ███ (███ ██ ████ █^███ )

████ ███████ ███████ ████ ██████████ ███████████ ███ █████████ ███████████████████ █████████