•State and prove Hall Effect?
When the magnetic field is applied perpendicular to the current carrying conductor then voltage is developed across the conductor.This voltage is known as hall voltage and the phenomena of production of hall voltage is called hall effect.
Consider a copper slab of width ‘d’ and thickness ‘t’ having and ‘n’ number of electrons per unit volume of slab. the area of slab is
A= d*t ……..1)
Let a current ‘I’ is applied from the face UPSC and a magnetic field ‘B’ is applied from the base PQRS then magnetic Lorentz forces acting on electron upward. so, upper facebecomes negatively charge whereas lower face becomes a positively charge. Due to the positive and negative charge ,an electric field is developed which opposees The Flow of electron. A voltage is developed when the electric force is balanced by the magnetic force. This voltage is known as Hall Voltage and denoted by VH.
Now, Electric force = magnetic force
eE = BeVsin90°
eE = BeV
V = E/B …….2)
Now, Current ‘I’ in a conductor is,
I = venA [Drift velocity]
V = I/neA ………3)
From equation 1 and 2, we get
I/neA = E/B
or, BI/neA = E
or, BI/neA = V/d
so, V = BI/net
This is required expression of hall voltage .
Application of Hall Effect:
1.It is to find no. of charge per. unit volume. [current density]
2. It is used to find magnetic flux density(B).
3.This effect is widly used in many devices as Hall senser.
4.It is used to the find sign of charge carrier.