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Unit 4 Day 8 – Ampere’s Law & Magnetic Fields thru Solenoids & Toroids

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. Definition of Current.

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Unit 4 Day 8 – Ampere’s Law & Magnetic Fields thru Solenoids & Toroids

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  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 μ0 was originally measured experimentally • To define μ0, 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 μ0 = 4πx 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 10-7N/m • Then, 1C = 1A·s, and the values of k & ε0were 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 Iencl 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

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