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Unformatted text preview: Let the rate of current rise dI/dt = a. The can thickness t, the number of turns of wire N,
the coil height h, the can’s conductivity 0, and the can radius R all enter into the
expression for the current In", induced in the can waist by the rising current I in the coil. (a) Assuming a given rate of current rise (I, assume the magnetic ﬁeld intensity inside
the coil (and can) is uniform and equal to the sheet current density of the coil. Use this
ﬁeld intensity to calculate the magnetic ﬁeld BCOIL as a function of coil current I and the appropriate dimensions.
shed runw K: I N" ’ H¢otb"" Buu,‘ —. [’01 T T (b) For a given rate of current rise a, use Faraday’s law and your expression in (a) to
calculate the voltage drop V= ﬁ E ' dz; along the circumference of the can. Express V
in terms of the rate of rise and other variables. é‘éLL: *i 3342: {Arr”11:31 ‘ M Ll» at» (c) The circumferential voltage around the can’s waist will induce a current [CAN in the
same direction circling the can waist. Let’s assume this current is restricted to the height
h of the coil (rather than spreading through the can). If the can’s conductivity is a, ﬁnd
an expression for the current ICAN. 3.
Run: 4L— ; 3‘“ 9 30 It”! : V“ wk kh‘”°(
"" am) his: _ o~t 613““
If: )_ YET (d) If you have time, use these parameters to ﬁnd a value for the can current 1cm: a = 1.5
x109A s",h=2cm,N=6,t=0.1mm,R=3.5 cm,and a: 3.57 x107 9'1 m‘1
(conductivity of aluminum). = 037W a'm“)(lo’\tu.)L?Sto‘1)(tnw’quw )(QXtSto‘kw‘)
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chguewi 5" WAS E M Texas State University—San Marcos
Ingram School of Engineering
EE3340: Fields and Waves
8 0 LU~T (o v S
Practice Problem 15: Electromagnetic Can Crusher NAME: DATE: One of the sillier things that can be done with powerful pulsed currents is to build
an electromagnetic can crusher, which does this sort of thing to aluminum drink cans: (from hgpd/membersﬁngom/extreme skier/cancrusherl) A can crusher works as follows. A highenergy pulse circuit (typically a highvoltage
capacitor discharging through a triggered spark gap) produces a steeply rising current
pulse through a coil wound around the waist of a can as shown: IU’) ...
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 Spring '11
 Stephen

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