New Magnetic Moment of Electron

 

Recently Physicists, calculated the electrons dipole moment which is almost 2.2 times more accurate than the previously measured. Actually they have measured the dipole moment with a precision of 0.13 parts per billion.

Here the first question is what exactly the dipole moment is and how it is calculated specially for electrons.

We all know, electrons revolves around the positively charged nucleus with a uniform velocity (again uniformity of velocity may be a prediction only). Let me here clear it, why I’m saying this, you know none of the scientist or physicists have ever seen an electron.

As per magnetic theory in a current carrying conductor, there will be a magnetic field around a straight current carrying conductor and also in a circular current carrying conductor. I think a common man who knows little about electrons and current, he or she definitely know that rate of flow of electrons is nothing but a current in a conductor. After knowing the definition of current, let me also tell you about the types of current.

1. Conduction current

2. Electronic Current

3. Displacement current

Ohhoooo, at this point of moment, I think, I should explain you in brief about these current, first one which is conduction current is most familiar to us and also the most important because dominant current in the circuit is the conduction current. The second one which is electronic current is not that important to us because we are least concerned about it. Actually in the direction of electrons flow, the electronic current flows and in the direction opposite to the flow of electrons, the conduction current flows. Hmmmm, the last one that’s the displacement current is defined by the famous scientist Maxwell in his famous Maxwell’s equations. To let you know more, this current is basically generated when there is a rate of change of electric flux with respect to the time.

Now, after knowing the definition of current and magnetic theory for a current carrying conductor. We can say very confidently, this uniform circular motion of electron is equivalent to a current loop which also possesses a magnetic dipole moment. 

What is this magnetic dipole moment. Hmmmmmm, it is nothing but Current times area vector.

M = I.A            (M is a vector quantity)

Equivalent current,                     

I = charge/time             

 

Orbital magnetic moment of the electron is

μ_l = I.A                                   (μ_l dipole moment of electron)

   

If electron revolves anticlockwise, the current associated flows clockwise.

As I said above that magnetic moment is a vector quantity, direction is 50% playing its role. To know the direction of magnetic dipole moment of revolving electron, we need to apply ampere’s right hand thumb rule, which says stretch the right hand and curl the fingers in the direction of current, the thumb will points towards the direction of μ_l.

If you know up to this, let’s relate μ_l with angular momentum (L) of the electron.

L = m_evr                 (direction of L is calculated by using screw rule)