1. Unit 4 Day 8 – Ampere’s Law & Magnetic Fields thru Solenoids & Toroids Definition of Current Ampere’s Law Magnetic Field Inside & Outside a Current Carrying Conductor Magnetic Field of a Solenoid Magnetic Field of a Toroid

2. Definition of Current The unit of current, Ampere, is defined in terms of the magnetic field it produces μ 0 was originally measured experimentally To define μ 0, a standard was created using two parallel wires, each with a current of I = 1.0 A, separated by a distance d = 1.0 m

3. Definition of Current The force between the wires per unit length is: using μ 0 = 4π x 10 -7 T·m/A exactly Therefore, 1A, by definition, is the current flowing in each of 2 long parallel wires, resulting in a magnetic force of 2.0 x 10 -7 N/m Then, 1C = 1A·s, and the values of k & ε 0 were then obtained experimentally

4. Ampere’s Law Remembering that the magnetic field in a long, straight current carrying conductor is: This equation is only valid for long straight wires. In general the relationship between current in a wire of any shape, and its magnetic field around it was derived by Andre Marie Ampere. For any arbitrary closed path around a current enclosed by the area of the closed path:

5. Ampere’s Law Where the integrand is taken around any closed loop, and I encl is the current passing through the area enclosed by the closed path For a straight conductor:

6. Magnetic Field Inside & Outside a Current Carrying Conductor Outside the conductor, the magnetic field is an inverse law: Inside the conductor, the magnetic field is linear because the current is uniformly distributed

7. Magnetic Field Inside & Outside a Current Carrying Conductor

8. Magnetic Field of a Solenoid A solenoid is a long coil of wire made of many (N) loops, each producing a magnetic field Inside the solenoid, the magnetic field is parallel to the long axis Outside the solenoid, the magnetic field is zero The magnetic field on-axis is:

9. Magnetic Field of a Toroid The magnetic field is confined to being inside the ring only The magnetic field is not uniformly distributed inside the ring; it is largest along the inner edge of the ring, and smallest at the outer edge of the ring Outside the ring the magnetic field is zero The magnetic field is all inside the coil, made of N loops of wire