The magnetic field in a region is given by $\overrightarrow{ B }= B _{0}\left(\frac{ x }{ a }\right) \,\hat{ k }$. $A$ square loop of side $d$ is placed with its edges along the $x$ and $y$ axes. The loop is moved with a constant velocity $\overrightarrow{ v }= v _{0} \hat{ i }$. The emf induced in the loop is:

• A
  $\frac{ B _{0} v _{0}^{2} d }{2 a }$
• B
  $\frac{ B _{0} v _{0} d }{2 a }$
• C
  $\frac{ B _{0} v _{0} d ^{2}}{ a }$
• D
  $\frac{ B _{0} v _{0} d ^{2}}{2 a }$