A long straight wire of radius R = 1 cm carries a total current I = 1 Amp

which flows uniformly through the cross-section of the wire. Draw a diagram of this wire and the
current and the magnetic field which is produced. Using Ampere’s law solve for the magnitude of
the magnetic field as a function of the radial distance for both the cases r < R and r > R. With
pencil and paper, plot this magnitude as a function of the radial distance r (with the vertical
coordinate being |~B| and the horizontal coordinate being r).

To draw the diagram, follow these steps:

1. Start by drawing a straight line to represent the wire. Label it as a long straight wire.
2. Mark a point at the center of the wire to represent the radial distance r = 0.
3. Draw arrows along the wire to indicate the direction of the current flow. Label it as I.
4. For the case of r < R (inside the wire), draw concentric circles around the wire to represent the magnetic field lines. These circles will have radii from 0 to R.
5. For the case of r > R (outside the wire), draw concentric circles around the wire with radii greater than R.

Now let's move on to solving for the magnitude of the magnetic field:

Inside the wire (r < R):
1. Apply Ampere's Law, which states that the line integral of the magnetic field around a closed loop is equal to the product of the current enclosed by the loop and the permeability of free space (μ0).
2. Choose a circular loop with a radius r (where r < R) centered around the wire. The current enclosed by this loop is the total current I.
3. The magnetic field B is constant along the loop and points perpendicular to the plane of the loop according to the right-hand rule.
4. The line integral of the magnetic field B can be simplified to the product of B and the circumference of the loop, which is 2πr.
5. Set the line integral equal to μ0 times the total current I: B * 2πr = μ0 * I.
6. Solve for the magnitude of the magnetic field in terms of r: B = (μ0 * I) / (2πr).

Outside the wire (r > R):
1. Choose a circular loop with a radius r (where r > R) centered around the wire. The current enclosed by this loop is the total current I.
2. The magnetic field B is constant along the loop and points perpendicular to the plane of the loop according to the right-hand rule.
3. The line integral of the magnetic field B can be simplified to the product of B and the circumference of the loop, which is 2πr.
4. Set the line integral equal to μ0 times the total current I: B * 2πr = μ0 * I.
5. Solve for the magnitude of the magnetic field in terms of r: B = (μ0 * I) / (2πr).

Now, using pencil and paper, you can plot the magnitude of the magnetic field as a function of the radial distance r, with the vertical coordinate as |~B| and the horizontal coordinate as r.