A metal wire of mass m slides without friction on two rails spaced at a distance d apart. The track lies in a vertical uniform magnetic field B. A constant current I flows along one rail, across the wire and back down the other rail. If the wire is initially at rest, the time taken by it to move through a distance x along the track is 

• A

  $\mathrm{t}=\sqrt{\frac{\mathrm{BId}}{2\mathrm{xm}}}$

• B

  $\mathrm{t}=\sqrt{\frac{2\mathrm{xm}}{\mathrm{BId}}}$

• C

  $\mathrm{t}=\sqrt{\frac{\mathrm{BIdm}}{2\mathrm{x}}}$

• D

  $\mathrm{t}=\sqrt{\frac{2\mathrm{dm}}{\mathrm{BIx}}}$