Physics Exam Review Notes: Magnetic Fields and Forces

LON-CAPA Homework and Exam Results

  • LON-CAPA HW 6 due on Wednesday, April 9, at 11:59 PM.
  • Exam 2 results posted:
    • Average score: 74%.

Magnetic Fields and Electric Current

  • Current in a solenoid (wire wrapped around a cylinder) creates a magnetic field similar to a bar magnet.
  • Source of magnetic fields:
    • Not a magnetic charge, but electric charge in motion (current).
  • Important to understand the currents to discern the magnetic field generated by a bar magnet.

Effects of Magnetic Fields on Moving Charges

  • Magnetic fields are detected by their effects on moving charges.
  • The force on a charge moving in a magnetic field is described by:
    • extbfFextMAG=q(extbfvimesextbfB)extbf{F}_{ ext{MAG}} = q ( extbf{v} imes extbf{B})
  • Where:
    • extbfFextMAGextbf{F}_{ ext{MAG}} = magnetic force
    • qq = charge
    • extbfvextbf{v} = velocity of the charge
    • extbfBextbf{B} = magnetic field

Observations about the Magnetic Force

  • The direction of the magnetic force is:
    • Perpendicular to both the velocity of the charge and the magnetic field direction.
  • If both electric field (E-field) and magnetic field (B-field) are present:
    • Total force on a charge is given by:
    • extbfF=qextbfE+q(extbfvimesextbfB)extbf{F} = q extbf{E} + q( extbf{v} imes extbf{B})

Example Problem with Electron in Fields

  • An electron moves through uniform fields E and B in the +x and +y directions; if there’s no net force, its velocity must remain:
    • Choices: A. +x-direction, B. +y-direction, C. -x-direction, D. +z-direction, E. -z-direction
  • Note: Since the electron is negatively charged, the direction of the forces will be reversed.

Force on Charged Particles Entering Magnetic Fields

  • When a charge qq enters a magnetic field with velocity vv:
    • The resultant path of the charge is circular due to the magnetic force being perpendicular to the velocity.
  • This phenomenon is described by the Lorentz force:
    • extbfF=qextbfvBextbf{F} = q extbf{v}B
  • Also useful in centripetal acceleration:
    • a=v2Ra = \frac{v^2}{R}
    • F=maF = ma
    • Relating forces: qvB=mv2RqvB = \frac{mv^2}{R}
    • Rearrangement gives R=mvqBR = \frac{mv}{qB}

Calculating Velocity Using Potential Difference

  1. Accelerate an electron through a potential difference riangleVriangle V:
    • mv=qriangleVmv = q riangle V
  2. When the magnetic field BB is turned on, rearranging gives:
    • R=mqriangleV2R = \frac{m}{q}\frac{ riangle V}{2}

Magnetic Field Directions in Chambers

  • In a setup of interconnected chambers:
    • When a positively charged particle takes a specific path, using the right-hand rule can help determine the magnetic field's direction:
    • Force is calculated using: extbfF=q(extbfvimesextbfB)extbf{F} = q( extbf{v} imes extbf{B})
  • This concept can apply to multiple chambers with different magnetic fields.

Forces on Current-Carrying Wires

  • For a long straight wire carrying current II in a magnetic field BB:
    • The force on this wire is described by:
    • extbfF=IextbfLimesextbfBextbf{F} = I extbf{L} imes extbf{B}

Magnetic Field due to a Current-Carrying Wire

  • Use the right-hand rule to find the direction of the magnetic field around a current-carrying wire:
    • Thumb represents current direction; fingers curl in the direction of the magnetic field.
    • This results in circular field lines around the wire.
  • The magnetic field's effects on points above/below the wire can be determined based on the orientation of current and field lines.