The magnetic field inn a region is given by `vec B = (B_0)/(L) y overset^k` where L is a fixed length. A conducting rod of length L lies along the Y - axis between the origin and the point (0,L, 0). If the rod moves with a velocity `v= v_0 overset^i`, find the emf induced between the ends of the rod.

Explanation

`vecB=(B_0)/(L)y hat k `
`L =Length rod on y axis `
`V=V_) hat i`
`Considering a small length dy to the rod`
`dE=BVdy`
` implies dE=(B_0)/(l) yxxV_0xxdy`
` implies dE=(B_0V_0)/(L)ydy`
`E=(B_0V_0)/(L)=[(y^2)/(2)]_(0)^(L)`
`=(B_(0)L_(0))/(L) (L^2)/(2)`
`=1/2 B_0 V_0 L.`