2
60kviews
What is Hall Effect? Derive expression for Hall voltage.
1 Answer
10
8.1kviews
written 8.2 years ago by |
Hall effect.
- Hall effect is the production of voltage across an electrical conductor, transverse to an electric current in the conductor and a magnetic field perpendicular to the current
The above figure shows a conductor placed in a magnetic field (B) along the z-axis. The current (I) flows through it along the x-axis
Hall voltage $(V_H)$ is developed along y-axis with electric field intensity $E_H$.
At Equilibrium,
(Force due to Hall voltage on charge carriers)=(Force due to magnetic field)
$qE_H = Bqv$
Where,
q = Magnitude of current
v = Drift velocity.
$E_H = \frac{V_H}{d}$
But, $\frac{V_H}{d} =Bv$
$IeV_H = B.v.d….(i)$
Let n.e be the charge density,
Now, I=(n.e)(w.d).v
$v = \frac{I}{n.e.w.d} ......(ii)$
From (i) and (ii)
$V_H = B.\frac({I}{n.e.w.d})d$
$V_H = \frac{BI}{new}$
This is the required expression for Hall voltage.
If $J = \frac{I}{wd}= Current \ \ density$
Hall voltage can also be written as
$V_H = \frac{BJd}{ne}$
ADD COMMENT
EDIT
Please log in to add an answer.