Question

Constants I Periodic Table Part A In a probe that uses the Hall effect to measure magnetic fields, a 13.6 A current passes through a 1.74 cm -wide 1.14 mm-thick strip of sodium metal. If the Hall emf is 1.86 μν , what is the magnitude of the magnetic field (take it perpendicular to the flat face of the strip)? Assume one free electron per atom of Na, and take its specific gravity to be 0.971. Submit Request Answer

Answer 1

Given that current (I) = 13.6 A thick strip of sodium = 1.74 cm wide 1.14 mm The volume occupied by Na atom is V = M/S Here M is the mass and S is the specific gravity V = 22.99 g/0.971 g/cm^3 V = 23.67 cm^3 The electron density is n = N/V Here N is the Avagadro number eta = 6.02 times 10^23/23.67 cm^3 = 6.02 times 10^23/23.67 cm^3 [1 m/100 cm]^3 eta = 2.54 times 10^28 electrons/m^3 Thus the magnetic field is B = V_H nqt/I Here V_H = the Hall voltage q = charge t = thickness and \r\n I = current B = (1.86 times 10^-6 v)(2.54 times 10^28 electrons)m^3)(1.6 times 10^-19 c)(1.14 times 10^-3)/13.6 A = (1.86 times 10^-6) times (2.54 times 10^28) times (1.6 times 10^-19)(1.14 times 10^-3)/13.6 = 8.6173056/13.6 B = 0.6336 T therefore magnitude of magnetic field (B) = 0.6336 T