Question

PHYS 2426 Engineering Physics II Problem 26.6 1. An ionized gas (such as hydrogen) is a collection of large numbers of electrons and protons. Such a collection of charged particles is called a "plasma". Assume such a plasma is contained in a cylindrical container of radius R 0.120 m and length 2.00 m. The current density in this plasma column is given by J ) = Jo(1-T/R) where Jo = 6000 A/m2 and is the radial variable. (a) Calculate the total current carried by this plasma column. (b) Calculate the resistance of the plasma column if the applied voltage is Vapplied 75.0 V.

Answer 1

NA Solo: Given douta: i) R = 0.120m ii) b = 2.00m ,ili) Jo= 6000 A/m2 and 1(x) = o(l-rR a) now taking & a thin ring of radius r and thickness ar then area of this circular strip dA= 20 r dr And current through this strip. dl=j xd/A or di = Joll - 7 (aar dr) = 1 J. (1 gr dr Now total current can be calculated by integration le 1 Sorgu- rdr or I any fir- oder = 20) or I = 24 J. ( = 20). Ce şJ = 21J (B) - 1 * J R² I hence I = { XT X6000x60.120) = 90.5 A b) Here 1 = 90.5A, V= 75.0 volt hence resistance R is given esha - 756 = 0.829B LOVIY