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Force on a Moving Charge

A charged particle experiences a force when moving perpendicular to a magnetic field. Force on a Moving Charge. F=qvB sin θ. q = the amount of charge in motion in the magnetic field v = the velocity the charge in the magnetic field B = the magnetic field strength

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Force on a Moving Charge

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  1. A charged particle experiences a force when moving perpendicular to a magnetic field. Force on a Moving Charge F=qvB sinθ q = the amount of charge in motion in the magnetic field v = the velocity the charge in the magnetic field B = the magnetic field strength θ = the angle between the velocity direction and magnetic field The force, charge velocity direction, and magnetic field direction are all perpendicular to each other. Direction conventions: x: into the page (-z) • : out of the page (+z) B x x x x x x x x x v F x B velocity out of the page force into the page Field lines out of the page Field lines into the page

  2. First Right Hand Rule • Used to determine the velocity direction, force direction, and magnetic field direction for a charge in motion in a magnetic field. • The right hand rule is used for positive charges. force velocity magnetic field

  3. Example Problem • A proton moves at 3.0x105 m/s in the positive-x direction while a 4.5 T magnetic field acts in the negative-y direction. What is the magnitude and direction of the force exerted on the proton? F=qvBsinθ=(1.6x10-19C)(3.0x105 m/s)(4.5 T) sin90°=2.2x10-13 N • Use the first right hand rule to determine the force direction on the charge. • -z direction

  4. What is the resulting motion of a charge in a magnetic field? v - F What is the direction of the magnetic field surrounding the charge?

  5. Force on wire in a magnetic field A current in a wire constitutes charges in motion. + + + + + + + I L F = qvBsinθ=q(L/t)B sinθ= (q/t)LBsinθ= BILsinθ F=BILsinθ F=force on the wire from the external magnetic field B = The external magnetic field that surrounds the wire I = current in the wire L=length of wire in the magnetic field θ = angle between the current direction and magnetic field. The direction of the magnetic field can be determined by the right hand rule with the current I, replacing the velocity direction.

  6. Example problem • A wire length carries 6.5 A of current along the positive-x axis while in a magnetic field of 7.0 T directed towards the positve-z axis. A length of 18 cm of wire is exposed to the magnetic field. What is the magnitude and direction of the force on the wire? • F=BILsinθ = (7.0 T)(6.5 A)(.18m)sin 90° • F=8.2 N • Use the right hand rule to determine the direction of the force. • Force direction: -y

  7. An Applications of Force on a Wire –Simple Internal Diagram of an Electric Motor Motor – a device which converts energy to mechanical motion Metal brushes inside ring I I S x N •

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