Static Fields: Fall-2025
HW 10 Practice: Due W5 D5
- Energy of Four Charges
Three charges are situated at the corners of a square (side \(s\)). Two have charge \(-q\) and are located on opposite corners. The third has charge \(+q\) and is opposite an empty corner.
- How much work does it take to bring in another charge, \(+q\), from far away and place it at the fourth corner?
- How much work does it take to assemble the whole configuration of four charges?
- Magnetic Field and Current, Version II
Find the volume current density that produces the following magnetic field (expressed in cylindrical coordinates): \begin{equation} \vec{B}(\vec{r}) = \begin{cases} \dfrac{\mu_0\,I\,s}{2\pi a^2}\hat{\phi}& s\leq a \\\\ \dfrac{\mu_0\,I}{2\pi s}\hat{\phi}& a<s<b \\\\ 0& s>b \end{cases} \end{equation} What is a physical situation that corresponds to this current density?
- Curl
Shown above is a two-dimensional cross-section of a vector field. All the parallel cross-sections of this field look exactly the same. Determine the direction of the curl at points A, B, and C.
- Symmetry Arguments for Amp\`ere's Law Use good symmetry arguments to find the possible direction for the magnetic field due to a current carrying wire. Also, use good symmetry arguments to find the possible functional dependence of the magnetic field due to a current carrying wire. Rather than writing this up to turn in, you should find a member of the teaching team and make the arguments to them verbally.