Answer to Question #192781 in Electricity and Magnetism for benjamin johnson

Question

Explain why the Hall effect occurs when a wire with a square cross-section of side length w carrying charges moving with a drift velocity vd is placed in a uniform magnetic field B orientated perpendicular to the side of the wire. Give an expression for the magnitude of the Hall voltage produced in this case

Answer 1

Gives

Drift velocity J=neV_d

_{we know that}

hall constant R_H$=\frac{E_H}{J_xB_z}\rightarrow(1)$

$R_H=\frac{1}{nq}\rightarrow(2)$

Then we know that

eqution (1)and(2) we can write as

$R_H=\frac{1}{nq}=\frac{E_H}{J_xB_z}$

Wire is square type

Hall electric field $E_H=\frac{V_H}{w}$ $\rightarrow(3)$

$E_H=R_HJ_xB_z$$\rightarrow(4)$

Current density $J_x=\frac{I_x}{A}\rightarrow(5)$

eqution(3)(4)and(5) we can write as

Then hall voltage

$V_H=E_Hw$

w=sample weight