# PHYS-222 Worksheet 10 for Section 25 &amp; 36 Problem 10-1 ```PHYS-222 Worksheet 10 for Section 25 &amp; 36
TA: Yang Li, leeyoung@iastate.edu
October 15, 2012
Problem 10-1
In Fig. (a) and (b), what are the directions of the induced current repectively in the loop? (assume we look
below at the loops)
A. CCW, CCW
B. CCW, CW
C. CW, CCW
D. CW, CW
Problem 10-2
A railgun (See the figure below) comprises a pair of parallel conducting rails, along which a sliding metallic
armature is accelerated by the electromagnetic field generated by the current carried on the rails . For
simplicity, suppose the armature can be modeled by a metallic bar with length d. We further assume the
magnetic field is uniform and proportional to the current I, B = k0 I. The effective resistance of the railway
plus the armature is R. The length of the railway is L. The voltage between two rails is V .
a. If at one time instant, the speed of the armature is v, what is the current I? Express your answer in
V
terms of v, V, R, d, L, k0 . I = R+k
0 dv
b. What is its acceleration a? Express your answer in terms of v, V, R, d, L, k0 . a =
V 2 k0 d
m(R+k0 dv)2
c∗ . With the relation between a and v, calculate the final velocity vf of the armature. vf '
R
k0 d ,
2
2P0 τ
1
2
2 mv0
14
v0
where v0 =
P0 = V /R, τ = L/v0 , assumming vf v0 . The meaning of v0 is the speed when the
resistance voltage equals the magnetic induction emf.
d∗ . Suppose the radius of the rails are a. Calculate k0 in terms of a, d, &micro;0 . k0 =
&micro;0 ln(d/a−1)
2πd
Figure 1: A railgun is an projectile launcher powered by electromagnetic field
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