Gauss’s Law and Electric Potential Homework Set Problem 1. A cube with 1.4 m edges is oriented as shown below in a region of uniform electric field. Find the electric flux through the right face if the electric field, in newtons/coulomb, is given by a) 6.00 i b) -2.00 j and c) -3.00 j + 4.00 k d) What is the total flux through the cube for each of these fields? z

y 1.40 m

x

Calculate the area of the right face of the cube (at y=1.4 m)

Write the direction of normal to the surface of the right face of the cube (Hint: i, j, or k)

Write an express of the flux Φ as a function of the scalar product of the electric field E and the area of the normal surface A

For each of electric fields, show the calculation of the electric flux below

Gauss’s Law and Electric Potential Homework Set

For the electric field give in part a) calculate the flux through each face of the cube. (Be sure to pay attention to the sign of the normal vector i.e. the left side of cube’s normal vector is –i)

Sum the fluxes that were determined in the previous part.

Based on your calculation of the total flux using the E-field in part a), please infer what the total fluxes using the electric fields of b) and c)

Under what could conditions would the total flux not be the value calculated in the previous section?

Gauss’s Law and Electric Potential Homework Set

Problem 2 Gauss’ Law for Gravitation is

in which ΦG is the net flux of the gravitational field g though a Gaussian surface that encloses menclosed. The field g is defined to be the acceleration of a test particle on which exerts menclosed gravitational force. Derive Newton’s Law of Gravitation from this. What is the significance of the minus sign? Assume that the field is created by a uniform spherical shape. In the notes,

is

evaluated. Write that evaluation below.

For the derived expression, substitute E with g and write the new expression below.

Insert the new expression into

and solve for g.

Let menclosed equal the mass of Earth. Derive the gravitational force acting on a particle of mass m.

What is the significance of the minus sign? Why is there no such explicit sign in the electrical version of Gauss’ Law?

Gauss’s Law and Electric Potential Homework Set

Problem 3. A long thin-walled cylindrical shell has an inner radius of b and an outer radius of c. Within the shell a solid charged cylinder of radius a (b>a) is placed in a concentric orientation. Both have a charge +q distributed uniformly within them. What is the magnitude of the electric field when a) r