Aptitude Test Problems in Physics Science for Everyone by S Krotov ( PDFDrive.com )

Solutions 279

Let us now write the equation of motion for

the jumper (over a small distance Ax):

B

ma.F.^

2d2v

R•

Considering that a = Av/At and v = Ax/At, we
obtain

m Av=

B 2 d 9 Ax

It can be seen that the change in the velocity of
the jumper is proportional to the change in its
x-coordinate (at the initial instant, xo = 0). There-
fore, the total change in velocity Vf =Vo = 0 —
vo = — vo is connected with the change in the
coordinate (with the total displacement s) through
the relation

B 2 d 2 s

m (-- vo)= •

Hence we can determine the length of the path
covered by the jumper before it comes to rest:

mRvo
s —
B 2 d 2

When the direction of the magnetic induction
B forms an angle a with the normal to the plane
of the rails, we obtain

rnRvo

s —

B 2 d 9 cost a '

Indeed, the induced emf, and hence the current
through the jumper, is determined by the magnetic
flux through the circuit, and in this case, the flux
is determined by the projection of the magnetic
induction B on the normal to the plane of the
circuit.
3.49. The lines of the magnetic flux produced by
the falling charged ball lie in the horizontal plane.
Therefore, the magnetic flux (DB through the sur-

R