You have a great summer job in a research laboratory with a group investigating

Question

You have a great summer job in a research laboratory with a group investigating the possibility of producing power from fusion. The device being designed confines a hot gas of positively charged ions, called plasma, in a very long cylinder with a radius of 2.0 cm. The charge density of the plasma in the cylinder is 6.0 x 10-5 C/m3. Positively charged Tritium ions are to be injected into the plasma perpendicular to the axis of the cylinder in a direction toward the center of the cylinder. Your job is to determine the speed that a Tritium ion should have when it enters the plasma cylinder so that its velocity is zero when it reaches the axis of the cylinder. Tritium is an isotope of Hydrogen with one proton and two neutrons. You look up the charge of a proton and mass of the tritium in your trusty Physics text to be 1.6 x 10-19 C and 5.0 x 10-27 Kg

Explanation / Answer

calculate electric potential energy difference dPE=1/2*m*v^2 where v=velocity at entrance

and velocity at centre=0

for electric potential difference ,calculate Electric field perpendicular to cylindrical axis using gauss law and chose cocentric cylindrical guassian surface

for r=R=2cm to r=0 ( L= length, integral is written as %u222B ,Q=total charge=L*y where y=linear charge density=%u03C0 *R^2*6.0*10^-5 C/m=%u03C0 *4*6.0*10^-9 C/m)

%u222B E.dA=qin/%u03F5

2*%u03C0 *r*L*E(r)=L*y*r^2/(R^2*%u03F5) where,R=2

E(r)=y*r^2/(2*%u03C0 *r*4*%u03F5)=y*r/(8*%u03C0 *%u03F5)

dPE=%u222Bq*y*r/(8*%u03C0 *%u03F5) from r=2 to r=0 cm

=(q*4*%u03C0 *6*10^-5)*4/(16*%u03C0 *%u03F5)=(q*6*10^-5)/%u03F5=1/2*m*v^2

v=sqr_root((2*q*6*10^-5)/%u03F5*m)=sqr_root((12X10^-9X1.6X10^-19)/(5X10^-27X%u03F5))

  C^2*m^2/kg unit

dont remember the vaue of %u03F5

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