A conducting bar moves on two conducting rails as shown in the figure. A constant magnetic field B exists into the page. The bar starts to move from the vertex at time $$t = 0$$ with a constant velocity. If the induced EMF is $$E \propto t^n$$. then value of n is _.

Let the semi-vertical angle of the V-shaped rails be $$\theta$$.

At time $$t$$: $$v = \text{constant}$$

$$x = vt$$

Effective length of the bar between the rails: $$l = 2x \tan\theta$$

$$l = 2vt \tan\theta$$

Motional EMF: $$E = Blv$$

$$E = B(2vt \tan\theta)v$$

$$E = 2Bv^2t \tan\theta$$

$$E \propto t^1$$