Question

Z b

sin xdx = cos a − cos b                                                                         (1)

a

They can then be referred to later in the text by number (see Equation 1).

1     Magnetic field of a uniformly charged wire

For this problem we will have a very long, thick, current carrying wire. The center of this wire is along the z-axis. And the wire has a radius R. The current density (current per unit area) of this wire is:

~j(r) = j0kˆ

where r is the distance from the z-axis, and j0 is a constant.

1. Determine the value of the constant j0 if the total current in the wire is I.

2. Use the same method we developed in class to determine the magnetic field of this wire.

2     Comparing the magnetic field of different long, straight wires

Create a plot of the magnetic field magnitude vs. distance from the center of the wire for each of these wires:

• Thin wire carrying a current I.

R

• Thick wire with radius R and current density ~j(r) = j1  1 − r   kˆ.

• Thick wire with radius R and uniform current density j0.

Choose the constants j1 and j0 so that all three wires have the same current. Comment about the similarities and differences in your plots.

Answer 1

1. Current Density =

Total current = I

Area of the face of wire =

I = current density X area =

Applying Ampere's law , we can find B as function of r

2. Comparing B field

a. For thin wire carrying current I

b.

Inside wire r < R

= = C1 r - C2 r^2

Outside wire

c. Thick wire Radius R, carrying current density

Here B has to be evaluated seperately inside the wire and outside

If we consider point at distance r from center of the face of wire

For r > R