Question #42920

A flexible conducting wire forms a closed loop in the $xy$-plane. At time $t=0\text{ s}$, the loop is a point at the origin $(0,0)$. For $t > 0\text{ s}$, the loop expands such that it always forms a circle passing through the origin, with its center moving along the positive $x$-axis at a constant velocity $v_0\text{ m s}^{-1}$. A non-uniform, static magnetic field exists in the region, given by $\vec{B} = \alpha x^2 \hat{k}$, where $\alpha$ is a positive constant in $\text{T m}^{-2}$ and $x$ is the position coordinate in meters. Which of the following represents the magnitude of the induced electromotive force (EMF) in the loop at time $t$?