Hence we obtain
mg sin a
a =
Cb 2 B 2 cosy a 'Solutions (^283)
3.53. During the motion of the jumper, the mag-
netic flux across the contour "closed" by the jumper
varies. As a result, an emf is induced in the con-
tour.
During a short time interval over which the
velocity v of the jumper can be treated as constant,
the instantaneous value of the induced emf is
—
At
— /AB cos a.
The current through the jumper at this instant is
I = A q
At '
where Aq is the charge stored in the capacitor during
the time At, i.e.
Aq = C A1S = CbB Ay cos a
(since the resistance of the guides and the jumper
is zero, the instantaneous value of the voltage
across the capacitor is 19. Therefore,
Av
/ = ChB (—) cos a= CbBa cos a,
At
where a is the acceleration of the jumper.
The jumper is acted upon by the force of gravity
and Ampere's force. Let us write the equation of
motion for the jumper:
ma = mg sin a — IbB cos a = mg sin a
—Cb 2 B 2 a cog a.
The time during which the jumper reaches the
foot of the "hump" can be determined from the con-
dition 1 =--
1/-
a i
-1
mg sin a(^7 21)
(m C12 1 .81 cos, a).