Energy Density of the a Magnetic Field

“Live as if you were to die tomorrow. Learn as if you were to live forever.” 

• From analysis of the energy stored in a conductor,

• The energy density(energy/volume) is:

• So the energy density stored in the magnetic field is:

• This equation gives density of stored energy at any point where the magnitude of the magnetic field is B.


• The energy density in a vacuum:

Reformulation of Faraday’s Law

 From the previous two expressions for work :

more generally:

Induced Electric Fields

• A changing magnetic field produces an electric filed. 

• Consider a particle of charge q moving around the circular path

Induction and Energy Transfers

What is the origin of the electric generated by induction?

•   Mechanical work  

 

 

Energy Stored in a Magnetic Field

we know that when some system that perform activity/work, energy needed. so, what about energy stored in magnetic field?

• Magnetic field-produced by electric current

• 2 charged particles of opposite sign-pulled away resulting electric potential energy ( stored energy that make that charged come closed as we released them)

• When a electric current is flowing in an inductor, there is energy stored in magnetic field

• Consider a pure inductor L, the instantaneous power which must be supplied to initiate the current in the inductor is:






So the energy input to built to a final current I is given by the integral:




total energy stored by an inductor L carrying current i


• noted that:  same expression applied to energy stored by a capacitor C and charged q:

Miss Inductance

If a current i is establish through each of the N winding of an inductor, a magnetuc flux links those windings.

Then, the inductance of the inductor is define as

The SI unit of inductance - henry (H)

1 henry = 1 H = 1 T.m^2/A

Inductance of solenoid

Consider along solenoid of cross sectional A. There will be inductance per unit length near its middle. 

So we must calculate the flux linkage set up by a given current.

And the given magnetic field there given ;

source : http://hyperphysics.phy-astr.gsu.edu

 Hence the inductance per unit length of a solenoid is

Noted that, this Miss Inductance is like capacitor, also depends only on geometry of the device. If we have triple of n thats mean we triple the flux each turns thus the inductance of L by a factor of 9.

WatCh Out.MR INDUCTOR is just in front of you.

Bismillah & Assalamualaikum

Here, i really love to share wif ol of u!!!

Becoz.. ‘sharing is caring’ ^-^

Hey, friends!

 Mr. INDUCTOR

Mr Inductosr~

~can produce desired magnetic field (-just like capacitor-)

~can store energy in magnetic field (-capacitor store energy in electric field-)

~in other words bulb in a circuit still can be light up for a while even we open(turn off) the switch.

With a very unique symbol

In a  solenoid -

As current flows in the wire(or any other conductor),

a magnetic field is produced and
 the voltage is induced.

these are very few informations about inductor before i'll share about inductance, for the next post.