(455) Equations for moving charges in magnetic fields [IB Physics SL/HL]

Moving Charge in a Magnetic Field

  • Magnetic Force Equation: F = QVB sin(Theta)

    • F: magnetic force (Newtons)

    • Q: charge (coulombs)

    • V: speed of the charge (m/s)

    • B: magnetic field strength (Tesla)

    • Theta: angle between velocity and magnetic field (degrees)

  • When Theta = 90°: sin(90°) = 1, thus F = QVB

    • Important to remember this relationship for calculations

Wire in a Magnetic Field

  • Magnetic Force Equation for Wire: F = BIL sin(Theta)

    • F: magnetic force (Newtons)

    • B: magnetic field strength (Teslas)

    • I: current in wire (Amps)

    • L: length of wire (meters)

    • Theta: angle between magnetic field and current (degrees)

  • For Theta = 90°: sin(90°) = 1, therefore F = BIL

Practical Applications

  • Questions involving ratios in magnetic forces are common in exams.

  • Example: If a wire has a current I in a magnetic field B perpendicular to the current, we use F = BIL.

  • Modified conditions: If current is I/8 and magnetic strength is 16B, then:

    • F2 = 2BI using ratios

    • Thus, if conditions change, magnetic force can be calculated accordingly.

Mass Spectrometers

  • Particles entering magnetic fields will deviate due to the magnetic force.

  • Helps in mass spectrometers to identify unknown particles based on their mass.

  • Example: Velocity selectors in spectrometers utilize magnetic curves to determine particle masses.

Military Applications

  • Magnetic Anomaly Detector (MAD) on military planes detects disturbances in Earth's magnetic field caused by submarines.

  • Practical use: locating submarines under the water surface.