Magnetic Field and Current

  • Static Fields 2022 (3 years) Consider the magnetic field \[ \vec{B}(s,\phi,z)= \begin{cases} 0&0\le s<a\\ \alpha \frac{1}{s}(s^4-a^4)\, \hat{\phi}&a<s<b\\ 0&s>b \end{cases} \]
    1. Use step and/or delta functions to write this magnetic field as a single expression valid everywhere in space.
    2. Find a formula for the current density that creates this magnetic field.
    3. Interpret your formula for the current density, i.e. explain briefly in words where the current is.