A rectangular loop with mass m, width 1 and resistance R falls vertically into a region with uniform magnetic field B pointed into the page. X X X X X X X X X X X l X X X X V= x B X X X X X X X (a) Show that, as long as the top side of the top has not entered the magnetic field, the terminal velocity is given by mgR (BI)² (b) Show that, for this terminal velocity u, the rate of change in gravitational potential energy is equal to the power dissipated via heat due to the resistance of the loop.
A rectangular loop with mass m, width 1 and resistance R falls vertically into a region with uniform magnetic field B pointed into the page. X X X X X X X X X X X l X X X X V= x B X X X X X X X (a) Show that, as long as the top side of the top has not entered the magnetic field, the terminal velocity is given by mgR (BI)² (b) Show that, for this terminal velocity u, the rate of change in gravitational potential energy is equal to the power dissipated via heat due to the resistance of the loop.
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Transcribed Image Text:A rectangular loop with mass m, width 1 and resistance R falls vertically
into a region with uniform magnetic field B pointed into the page.
X
X
X
X X X
X
X
X X
X
l
X
X
X
X
V=
X
x B
X
X X
(a) Show that, as long as the top side of the top has not entered the magnetic field,
the terminal velocity is given by
mgR
(Bl)²
(b) Show that, for this terminal velocity u, the rate of change in gravitational potential
energy is equal to the power dissipated via heat due to the resistance of the loop.
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