A small magnetic dipole with dipole moment \(\vec{\mu}\) is located at the center of a fixed, flat circular conducting loop lying in the \(xy\)-plane. Initially at time \(t = 0\), \(\vec{\mu}\) points in the \(+z\)-direction. The dipole is then forced to rotate at a constant angular speed \(\omega\) about the \(x\)-axis toward the \(+y\)-axis, such that its orientation is given by \(\vec{\mu}(t) = \mu \cos(\omega t)\hat{k} + \mu \sin(\omega t)\hat{j}\). Which of the following correctly identifies the direction of the magnetic field \(\vec{B}_{\text{ring}}\) produced at the origin by the induced current in the loop, and the direction of the magnetic torque \(\vec{\tau}\) exerted on the dipole by \(\vec{B}_{\text{ring}}\), at the instant \(\omega t = \dfrac{\pi}{2}\)?