Answer
$\frac{1}{2}\mu_{\circ}\lambda \omega$
Work Step by Step
We can find the required magnitude of the magnetic field as follows:
We know that $q=2\pi R\lambda$
Similarly $t=\frac{2\pi}{\omega}$
Now $I=\frac{q}{t}$
$\implies I=\frac{(2\pi R)\lambda}{\frac{2\pi}{\omega}}$
$\implies I=\lambda R\omega$
The magnetic field is given as
$B=\frac{\mu_{\circ}I}{2R}$
We plug in the value of I in the above equation to obtain:
$B=\frac{\mu_{\circ}(\lambda \omega R)}{2R}$
$B=\frac{1}{2}\mu_{\circ}\lambda \omega$
