Magnetism + Calculus + Mechanics = Megatulics

Let an Super Conducting Square Loop ( having negligible resistance ) and has Self inductance "L" and has mass of "m" and side length ll is released from rest in the gravity from the height "H" at time t=0.There is an infinitely Long current carrying wire which is in Same Plane of that of Square Loop and current I0{ I }_{ 0 } flowing in it.

Then Find The Velocity of the square loop when it is at height of H4\frac { H }{ 4 } from the wire.


Details and assumptions

m=1kgL=10henryl=1mI0=107Amp.H=2mg=9.8m/s2\bullet \quad m=1\quad kg\\ \bullet \quad L=10\quad henry\\ \bullet \quad l=1m\\ \bullet \quad { I }_{ 0 }={ 10 }^{ 7 }\quad Amp.\\ \bullet \quad H=2\quad m\\ \bullet \quad g=9.8\quad m/{ s }^{ 2 }.

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