D3 motion in magnetic fields

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9 Terms

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motor effect

  • when a current-carrying wire is placed in a magnetic field, the magnetic interaction between the conventional current and magnetic field results in a force.

  • F = BIL sin theta

    • sin theta is between B and I → max force at 90, no force at 0 (parallel)

    • units of B is tesla

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tesla

the magnetic flux density of 1 tesla will cause a wire of length 1m carrying current of 1A that is perpendicular to the field to experience a force of 1N

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magnetic field due to current carrying wire

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parallel current-carrying conductors

the current in each wire produces a magnetic field, the other wire is in the field so it experiences a force.

force per unit length calculated using Ampere’s force law: F/L

direction of magnetic field at any point is the tangent to the circular field.

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term image

  • magnetic field is out of paper

  • even though current rotates, angle between B and I is still perpendicular → sin theta same, magnitude of F same

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charges in magnetic fields on a microscopic level

  • each electron in the wire experiences force as it travels through magnetic field → note electron flow is opposite to conventional current

  • sum of forces causes total force on wire F = BIL

  • if per electron, F=Bqv

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motion of charged particle in magnetic field

  • F=qvBsintheta, if theta (angle between B and I) = 90, undergoes circular motion

    • magnitude of v unchanged but direction changes by FLHR

    • F provides centripetal force, work done = 0 since v is perpendicular to F at all times

    • magnetic force = centripetal force → r = mv sintheta/qB

  • if charged particle moves through magnetic field at an angle, experiences helical motion

    • perpendicular component vsintheta causes circular motion

    • parallel component vcostheta is uniform

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motion of charged particle in crossed electric/magnetic fields

parabolic motion

  • Fb and Fe balanced, Bqv = qE → v=E/B

  • F not perpendicular to v! just downwards all the time

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condition for charged particle to experience force in a magnetic field

velocity of charged particle must have a component perpendicular to the direction of the magnetic field