BIOT-SAVART’S LAW OR AMPERE’S LAW FOR CURRENT ELEMENT
Biot-Savart’s law deals with the magnetic field induction at a point due to a small current element. Current element
A current element is a conductor carrying current.It is the product of current,I and length of very small segment of current carrying wire ,dL. Let us consider a small element AB of length dl of the conductor RS carrying a current I. Let r be the position vector of the point P from the current element I dL.and θ be the angle dl and r. According to Biot-Savart’s law,the magnetic field induction dB or magnetic flux density at a point P due to current element depends upon the following factors. (i) dB∞I

(ii) dB∞dl
(iii) dB∞sinθ
(iv) dB∞1/r2
Combining these factors,we get
dB∞IdLsinθ/r2
or dB=K Idl sinθ/r2 where K is a constant of perportionality.
In S.I units, K=μ0/4π thus , dB=μ0/4π I dl sinθ/r2 where μ0 is absolute premeability of free space and
μ0=4π*10-7 Wb A-1m-1
= 4π*10-7*TA-1m [ 1T=1 Wb m-2] In C.G.S units,K=1 (In free space)
Thus dB=Idl sinθ/r2
In vector form,
dB=μ0/4π I(dl*r)/r3
magnetic field induction at point P due to current through entire wire is B=∫μ0/4πIdl*r/r3
Or B=∫μ0/4π Idl sin θ/r2 BiotSavart’s law in terms of magnetising force or magnetic intensity (H) of the magnetic field: In S.I System,
dH=dB/μ0=1/4π Idl*r/r3=1/4π Idl*αr/r2
H=∫1/4π Idl*αr/r2
H= ∫1/4π Idl sinθ/r2
Importance OF BIOT SAVART’S LAW:-
1. This law is analogous to Coulomb’s law in electrostatics. 2. Biot Savart’s law is valid for a symmetrical current distribution. 3. This law cannot be easily verified experimentally as the current carrying conductor of very small length cannot be obtained pratically. 4. Biot Sarvart’s law is applicable...

...
Evolutionary Bioenergetics of Protocells
Introduction
Bioenergetics is central to our understanding of living systems, though there has been very less research in field of finding the origins of life. Understanding the origin of cellular life on Earth requires the discovery of plausible pathways for the transition from complex prebiotic chemistry to simple biology, defined as the emergence of chemical assemblies capable of Darwinian evolution.
A coherent pathway which starts from no more than rocks, water and carbon dioxide and leads to the emergence of the strange bioenergetics properties of living cells has been traced back to what is now called as Protocells.
A Protocell is found to be the first form of a cell before true cells arose. They have a lipid protein and carry out energy metabolism. It is theorised that at the origin of life the first Protocells must have needed a vast amount of energy to drive their metabolism and replication, as enzymes that catalyse very specific reactions were yet to evolve. Most energy flux must have simply dissipated without use. Humans consume more than a kilogram (more than 700 litres) of oxygen every day, exhaling it as carbon dioxide. The simplest cells, growing from the reaction of hydrogen with carbon dioxide, produce about 40 times as much waste product from their respiration as organic carbon (by mass).
In all these cases, the energy derived from respiration is stored in the form of ion gradients over membranes.This...