State the magnetic field magnitude outside a long straight wire carrying current \(I\).

State the ideal magnetic field inside a long solenoid with turns per unit length \(n\) and current \(I\).

State the magnetic field inside a toroid with \(N\) turns carrying current \(I\), at radius \(r\) inside the core.

A long solenoid has \(n=800\,\mathrm{m^{-1}}\) and current \(0.50\,\mathrm A\). Find its internal field.

State the field inside a long wire of radius \(R\) carrying uniformly distributed current \(I\), for \(r<R\).

A wire of radius \(2.0\,\mathrm{mm}\) carries a uniform current \(10\,\mathrm A\). Find \(B\) at \(r=1.0\,\mathrm{mm}\).

The same wire carries \(10\,\mathrm A\). Find \(B\) outside the wire at \(r=5.0\,\mathrm{mm}\).

A toroid has \(500\) turns, current \(0.20\,\mathrm A\), and mean radius \(0.10\,\mathrm m\). Estimate the field at that radius.

For a long wire with uniform current density, explain why \(B\propto r\) inside the wire but \(B\propto 1/r\) outside it.

A coaxial cable has current \(+I\) in the inner conductor and return current \(-I\) in the outer conductor. Use Ampere's law to describe \(B\) outside the cable.