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Unit 4 day 2 – Forces on Currents & Charges in Magnetic Fields (B)

Unit 4 day 2 – Forces on Currents & Charges in Magnetic Fields (B). The force exerted on a current carrying conductor by a B-Field The Magnetic Force on a Semi-Circular Wire Force on an Electric Charge Moving through a B-Field Path of an Electric in a B-Field

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Unit 4 day 2 – Forces on Currents & Charges in Magnetic Fields (B)

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  1. Unit 4 day 2 – Forces on Currents & Charges in Magnetic Fields (B) • The force exerted on a current carrying conductor by a B-Field • The Magnetic Force on a Semi-Circular Wire • Force on an Electric Charge Moving through a B-Field • Path of an Electric in a B-Field • A Particle traveling in both an E- & B-Field

  2. The Force Exerted on a Current Carrying Conductor in a B-Field #2 • Not only does a current in a wire generate a magnetic field and exert a force on a compass needle, but by Newton’s 3rd Law, the reverse is also true. A magnet can also exert a force on a current carrying conductor

  3. Magnetic Force on a Current Carrying Conductor where l is the length of wire immersed in the magnetic field • This implies that the direction of the force is perpendicular to the direction of the B-Field (Right Hand Rule #2) • Then the maximum force is:

  4. Magnetic Force on a Current Carrying Conductor • If the direction of the current is not perpendicular to the B-Field, but rather at some angle θ then:

  5. Magnetic Force on a Current Carrying Conductor • The equation assumes the magnetic fields is uniform & the current carrying conductor does not make the same angle θwith B • SI Units for B-Field is Tesla (T) 1 T = 1N/A-m • We can explore the above equation in differential form: where dF is the infinitesimal force acting on a differential length dl of the wire

  6. Magnetic Force on a Semi-Circular Wire

  7. Force on an Electric Charge Moving Through a B-Field where Δt is the time for charge q to travel a distance l or the force on a particle is:

  8. Force on an Electric Charge Moving Through a B-Field • If , then the force is a maximum and • If the velocity is at some angle θ wrt the B-Field, then:

  9. Path of an Electron in a Magnetic Field • If , then the electron will move in a curved circular path, and the magnetic force acting on it will act like a centripetal force • The radius of the circular orbit will be: • The period for 1 revolution will be: • The Cyclotron Frequency is:

  10. Path of an Electron in a Magnetic Field • Note: if the Particle was a proton, the circular path would be upward (counter-clockwise)

  11. A Particle Traveling in Both an E- & B- Field • The force on a particle traveling in the presence of both an electric and magnetic field which are mutually perpendicular, is given by the Lorentz Equation: • For a particle to travel straight through, the net force on the particle must equal zero, yielding a velocity selector:

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