Solve the following using Gauss' Law and Coulomb's Law

Please answer in a very detailed way where slow learners would understand. Thank you so much!

the solution answer format: (see the example on the third picture.)

1. Given:
2. Find:

1. A cubic space (1.5m on each side) contains positively charged particles. Imagine that the space is surrounded by Gaussian surface of the exact same dimension as the cube and that the Efield caused by the charges is normal to the faces of Gaussian cube. If the Efield at each surface has magnitude of 760 MC, determine the number of charges per unit volume in the space described (ie., find the charge density. 2. A point charge of 2 microCoulomb at the center of the cube with sides L= 5cm. What is the net electric flux through the surface? 3. A charge is located inside the cube ( is not at the center) a. Find the net electric flux passing through the surface of the cube? b. Can you find the electric field on the surface of the cube using Gauss's Law? 4. A metal sphere of radius 10 cm carries a charge of + 2.0 microCoulomb uniformly distributed over its surface. What is the magnitude of the electric field due to this sphere at a point 5.0 cm outside the sphere surface? Electric field due to any arbitrary charge configuration can be calculated using 1. Coulomb's Law 2. Gauss Law If the charge configuration possess some kind of symmetry, then Gauss law is very efficient to calculate electric field What is Charge Density Formula? "The charge density is the measure of electric charge per unit area of a surface, or per unit volume of a body or field. The charge density tells us how much charge is stored in a particular field. Charge density can be determined in terms of volume, area, or length. Depending on the nature of the surface charge density is given as the following 1. Linear charge density 2. Surface Charge Density A = 9/1 O=q/A where: * = linear charge density where: o = surface charge density q= is charge q = charge |= length A = area SI Unit? Unit of linear charge density? SI Unit is Coulomb/m? or c/m 2 SI unit is Coulomb/meter or C/m 3. Volume charge density p = q/v q =charge SI unit? where: V= volume Coulomb/m3 p = volume charge density or C/mExample Find the charge density if a charge of 8 C is present in a cube of 4 m3 Solution Given Charge q = 8 C Volume v = 4m 3 Find: p =? p = q/v P = 8C 4m 3 3 p = 2 C/m