Question

The figure shows a portion of a silver ribbon with z_1 = 14.0 mm and y_1 = 0.21 mm, carrying a current of 120 A in the + x-direction. The ribbon lies in a uniform magnetic field, in the y-direction, with magnitude 0.90 T. Apply the simplified model of the Hall effect.

Answer 1

current inx-direction I = 120 A

uniform magnetic field, in the y-direction B = 0.9 T

and y1 = 0.21 mm = 0.21*10^-3 m

       z1 = 14 mm = 14*10^-3 m

charge of the electron q = 1.6*10^-19 C

a)

free electron density n = 5.85*1028 ele/m³

drift velocity vd = I/nqA    ............. (1)

     where, cross sectional area A = y1z1 = 2.94*10^-6 m²

substitute the given data in eq (1), we get

       v_d = 4.36*10^-3 m/s

b)

from Hall effet,

electric field E = v_dB    ........... (2)

substitute the given data in eq (2), we get

         E = 3.92*10^-3 V/m

c)

from right hand rule, we have magnetic force on

electrons are in positive Z-direction.

therefore, the electric field will be positive Z-direction.

d)

Hall emf = Ez1

                = (3.92*10^-3)(14*10^-3 )

               = 54.9*10^-6 V

                = 54.9 μV