**Hypothetical** thin conducting rod AB is sliding without friction on a parabolic Path:
$y={ x }^{ 2 }$.
in the X-Y plane from hight 'H' from vertex of parabola and where gravity also exist in -Y direction.

Also an uniform magnetic field exist in -Z direction. Such that it's Magnitude is 'B' . Now conducting Rod is released under gravity at time t=0.

This conducting rod has **Special Property** That it always remains just inside the Parabola. Which means its length reduced continuously to just fit in Parabola. In this Process linear mass density $'\lambda '$. of rod remains constant.

Then find the **induced emf** developed across the ends of conducting Rod at the instant when it reaches at hight$\frac { H }{ 2 }$ , from vertex of Parabola.

**Assumptions**

$\bullet$ When mass is continuously detached from rod with time then there is no extra impulse act's on rod.

$\bullet$ Conducting Rod Has **Infinitely Large Resistance**.

$\bullet$ No friction between rod and Parabola.

$\bullet$ In this Process linear mass density $'\lambda '$. of rod remains constant.

$\bullet$ Air resistance is negligible.

$\bullet$ Dark lines shown in figure is the conducting Rod at different different time.

$\bullet$ This is An Hypothetical Rod not Found on earth.

**Details**

$\bullet \quad B=0.5\quad T\\ \bullet \quad H=2\quad m\\ \bullet \quad g=10\quad m/{ s }^{ 2 }$.