8 questions

The value of at is given as . Determine the incremental work required to move a charge a distance of

a) in the direction of ;

b) in the direction of ;

c) in the direction of ;

d) in the direction of ;

e) in the direction of .

Question 2:

If , find the incremental amount of work done in moving a charge a distance of from

a) toward ;

b) toward .

Question 3:

Compute the value of for with and P(2, 1, 2) using the path

a) straight-line segments to to ;

b) straight-line segments

Question 4:

Let Given an initial point and a final point find using the path

a) straight line:

b) parabola:

Question 5:

Given the current density

a. Find the total current crossing the plane in the a y direction in the region .

b. Find the total current leaving the region by integrating over the surface of the cube.

c. Repeat part (b), but use the divergence theorem.

Question 6:

Let

a. Find the total current flowing through that portion of the spherical surface , bounded by

b. Find the average value of J over the defined area.

Question 7:

The current density in a certain region is approximated by .

a. At how much current is crossing the surface?

b. Repeat for

c. Use the continuity equation to find assuming that as .

d. Find an expression for the velocity of the charge density.

Question 8:

Two perfectly conducting cylindrical surfaces of length are located at and cm. The total current passing radially outward through the medium between the cylinders is dc.

Find the voltage and resistance between the cylinders, and E in the region between the cylinders, if a conducting material having S/m is present for