1. Applications of Ampere’s Law
Ex Field outside and inside a long straight current- carrying wire
Ex Field outside a current sheet
Ex Field of a solenoid
Fig Field of a toroidal solenoid
This lecture

2. EXAMPLE 26.8: A long straight wire of radius R carries a current I that is uniformly distributed over the circular cross section of the wire. Find the magnetic field both (a) outside and (b) inside the wire. I I

3. Magnetic field of a solenoid
We can use Ampere’s Law.
Take the loop with sides abcd and integrate along each side.
Only side ab contributes.
In bc and da, B is perpendicular to dl.
In cd B = 0 (approx).
Bh = μ0Ienc
Bh = μ0 i N
B = μ0 i n
(n = N/h, number of turns per unit length)

4. S N
Graph of the magnetic field on the axis inside a solenoid versus the position x on the axis. The field is nearly constant except near the ends.
Magnetic fields of a solenoid. They are identical to those of a bar magnet of the same shape.

5. Toroid
Read p457 Apply Ampere’s Law to circle of radius r

6. CHECKPOINT: The figure shows three long, straight, parallel, equally spaced wires with identical currents either into or out of the page. Rank the wires according to the magnitude of the force on each due to the currents in the other two wires.
Answer: B, C, A

7. CHECKPOINT: The figure shows three equal currents i, two parallel, one anti-parallel, and four Amperian loops. Rank the loops according to the magnitude of along
each, greatest first.
Answer: D, A = C, B