All Problems

Constant Magnetic Field, Magnetics

Problem 3.233

A direct current of density j flows along a round uniform straight wire with cross-section radius \(R .\) Find the magnetic induction vector of this current at the point whose position relative to the axis of the wire is defined by a radius vector \(\mathbf{r}\). The magnetic permeability is assumed to be equal to unity throughout all the space.

Reveal Answer
B={1/2μ0[jr] for r⩽R1/2μ0[jr]R2/r2 for r⩾R.\mathbf{B}=\left\{\begin{array}{l} 1 / 2 \mu_{0}[\mathbf{j r}] \text { for } r \leqslant R \\ 1 / 2 \mu_{0}[\mathbf{j r}] R^{2} / r^{2} \text { for } r \geqslant R . \end{array}\right.
Prev
Next