Aug 012013
 

When magnetic field is applied perpendicular to a current carrying conductor, then voltage is developed across the conductor in the direction perpendicular to both current and magnetic field. This effect is called Hall effect.hall effect

Let us consider a rectangular cross sectional specimen carrying current ‘Ix‘ in x-axis. Then electrons get drifted in opposite direction to the flow to current. Their velocity is ‘vx‘. Let uniform magnetic field ‘Bz‘ be applied on the specimen along z-axis. Let ‘θ’ be the angle between the direction of magnetic field and the plane of the conductor. Then each of the drifting electrons experience Lorentz force along negative y-axis which is given by
Fl = evxBzsinθ
   = evxBzsin90o
   = evxBz

The Lorentz force causes the electrons to bend downwards which will result to the collection of large number of electrons at the lower surface and deficiency of electrons at the upper surface. Therefore, downward electric field is generated, which is called Hall Field (EH).
The Hall field opposes the further downward movement of electrons. So, at steady state condition,

Electrostatic force = Lorentz force
or, e × Eh = evxBz
or, EH = vxBz …. (i)

The current density Jx is given by,

Jx = – nevx …. (ii), where the negative sign represents the nature of charge of electrons.
Dividing equation (i) by (ii), we get,

EHJx = vxBz– nevx
∴ EH = JxBz– ne

This gives the magnitude of Hall electric field.

Again,
EHJxBz = – 1ne
EHJxBz = RH, where RH is Hall coefficient or Hall constant.

Hall Constant

Hall constant is defined as the Hall field per unit current density per unit transverse magnetic field.
The applications of Hall Constant are:

  • Hall constant can be used to find out the concentration of charge.
  • It can be used to identify the nature of charge carrier.


Jul 312013
 


Moving coil galvanometer is a device which is used to detect and measure small electric currents present in an electric circuit.

Principle

It is based on the principle that, “When a current carrying coil is placed in magnetic field, it experiences torque.”

moving-coil-galvanometer radial-field

Construction

A moving coil galvanometer consists of a rectangular coil having large number of turns winded in a non-metallic frame with a soft iron as a central ore. The coil is suspended between two concave poles of two permanent magnets with the help of phosphor-bronze strip. The strip also acts as a path of current to the coil because it is connected to the terminal ‘t1‘ of the galvanometer. Other end of the coil is connected to a light spring which exerts small restoring couple on the coil and then it is finally connected to terminal ‘t2‘. A concave mirror is attached on the strip to note the deflection of the coil by using a lamp and scale arrangement.

Working Method

When current is passed to the coil through the terminals ‘t1‘ and ‘t2‘, the coil gets deflected due to torque on it. This deflecting torque on the coil is given by, τd = BINAcosθ

Since the poles of the magnet are concave, the magnetic field is radial, i.e. θ = 0o. Therefore,
τd = BINA

As the coil gets deflected, the suspension wire gets twisted and restoring torque is developed on it. Let, k be the restoring torque per unit angle of twist for the suspension wire, then the total restoring torque for an angle θ is
τr = kθ

For the equilibrium of the coil,

Deflecting torque (τd) = Restoring torque (τr)

or, BINA = kθ

or, I = kθBNA

∴ = Gθ, where G = kBNA is a constant for galvanometer.

Hence, in moving coil galvanometer, deflection is directly proportional to current.