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Facts to mem Physics Chapter 27 & 28

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  • Symbol and unit for magnetic field
    Magnetic field is represented by \(B\) and measured in teslas (T).
  • Symbol and unit for electric current
    Electric current is represented by \(I\) and measured in amperes (A).
  • Number of loops and its unit
    Number of loops is represented by \(N\) and is unitless.
  • Number of loops per length and its unit
    Number of loops per length is represented by \(n\) and measured in inverse meters (1/m).
  • Permeability of free space symbol and value
    Permeability of free space is \(\mu_0\) with value \(4\pi \times 10^{-7}~\mathrm{T \cdot m/A}\).
  • Magnetic force on a charged particle (vector form)
    Force on a charged particle in a magnetic field is \(\mathbf{F_B} = q \mathbf{v} \times \mathbf{B}\).
  • Magnetic force on a charged particle (magnitude)
    Magnitude of force is \(F_B = q v B \sin\theta\), where θ is angle between velocity and magnetic field.
  • Force on a current-carrying wire in a magnetic field (vector form)
    Force on wire is \(\mathbf{F_B} = I \mathbf{L} \times \mathbf{B}\).
  • Force on a current-carrying wire in a magnetic field (magnitude)
    Magnitude of force is \(F_B = I L B \sin\theta\), where θ is angle between wire and magnetic field.
  • Magnetic dipole moment of a wire loop
    Magnetic dipole moment is \(\mu = I A\), where A is loop area.
  • Torque on a magnetic dipole in a magnetic field
    Torque is \(\boldsymbol{\tau} = \boldsymbol{\mu} \times \mathbf{B}\).
  • Potential energy of a magnetic dipole in a magnetic field
    Potential energy is \(U = - \boldsymbol{\mu} \cdot \mathbf{B}\).
  • Magnetic flux through a surface
    Magnetic flux is \(\Phi_B = \int \mathbf{B} \cdot d\mathbf{A}\).
  • Magnetic field due to a long straight wire
    Magnetic field strength is \(B = \frac{\mu_0 I}{2 \pi r}\), where r is distance from wire.
  • Direction of magnetic field around a long straight wire
    Magnetic field forms circles around wire; use right hand with thumb in current direction and curled fingers show magnetic field direction.
  • Magnetic field at center of a wire loop
    Magnetic field strength is \(B = \frac{N \mu_0 I}{2 a}\), where a is loop radius.
  • Direction of magnetic field at center of wire loop
    Curl fingers in current direction; thumb points in direction of magnetic field at center.
  • Magnetic field inside a solenoid
    Magnetic field strength is \(B = \mu_0 n I\), where \(n = \frac{N}{L}\) is loops per length.
  • Characteristic of magnetic field inside a solenoid
    Magnetic field is approximately constant over the inner volume of the solenoid.
  • Force per unit length between two current-carrying wires
    Force per length is \(\frac{F}{L} = \frac{\mu_0 I_1 I_2}{2 \pi r}\), where r is distance between wires.
  • When do two parallel current-carrying wires attract or repel?
    Wires attract if currents flow in the same direction; repel if currents flow in opposite directions.
  • Ampere's Law equation
    Ampere's Law is \(\oint \mathbf{B} \cdot d\mathbf{l} = \mu_0 I_{\text{enclosed}}\).
  • Determining sign of enclosed currents in Ampere's Law
    Curl fingers in direction of \(d\mathbf{l}\); currents in thumb direction are positive, opposite are negative.
  • Equation explaining velocity selector operation
    Velocity selector satisfies \(q E = q v B\), balancing electric and magnetic forces.
  • Equation used in mass spectrometer
    Mass spectrometer relation is \(m v^2 / R = q v B\), relating mass, velocity, radius, charge, and magnetic field.