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In an experiment to determine the charge to mass ratio e/m of the electron using a cylindrical diode, the following equation is derived: e/m=8V/(r^2 B^2 ), where V is the potential difference across the diode of radius r at the critical field B. The latter is supplied by passing a current I through a solenoid of diameter D and length L, and is given by B = (μ_0 nI)/(I+D^2/L^2 )^(1/2) , where n is the number of turns per unit length. The appropriate experimental quantities are determined as follows:n = 3920 m–1; D = 0.035 + 0.001 m; L = 0.120 + 0.001 m;r = (3.4 + 0.1) × 10–3 m; 1 = 1.92 + 0.02 A; V = 20 + 1 V.
Value of e/m:
(a) 1.6 × 1011 C/kg
(b) 1.7 × 1011 C/kg
(c) 1.8 × 1011 C/kg
(d) 2.7 × 1011 C/kg
(b) e/m=8V/(r^2 B^2 ) =(8×20)/((3.4×?10?^(-3) )^2 (9.08×?10?^(-3) )^2 )=(160×?10?^12)/(3.4×9.08)^2 (160×?10?^12)/953 = 1.68 × 1011 C/kg = 1.7 × 1011 C/kg
(b)
= 1.68 × 1011 C/kg = 1.7 × 1011 C/kg
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