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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

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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 3 rd Law, the reverse is also true. A magnet can also exert a force on a current carrying conductor

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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:

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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:

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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 θ with 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

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Magnetic Force on a Semi-Circular Wire

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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:

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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:

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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:

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

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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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