The two conducting rails are placed perpendicular to each other, such that their ends are joined as shown in figure. A conducting bar is now placed over the rails and start moving with constant velocity v starting from the vertex at time t = 0.
(i) The flux through the triangle (isosceles) by the rails and bar at `t=t_(0)`.
(ii) The emf around the triangle at that time.
(iii) In what manner does the emf around the triangle vary with time.

Explanation

(i) At time = t, area of loop, S `=(1)/(2).vt.2vt=v^(2)t^(2)`
`(because"area of isosceles triangle"=(1)/(2)xx"base"xx"height")`
Using the relation,
Magnetic flux `phi_(B)=BS=Bv^(2)t^(2)andat,t=t_(0)rArrphi=Bv^(2)t_(0)^(2)`
(ii) The emf developed around the triangle at to,
further, `e=|(dphi_(B))/(dt)|=Bv^(2).2t=2Bv^(2)t`
At `t=t_(0),e=2Bv^(2)t_(0)`
(iii) According to the relation obtained for the emf
`i.e.," "e=2Bv^(2)trArrepropt`

Hence, emf varies linearly with time.