Jean-Baptiste Biot and Felix Savart jointly gave the Biot-Savart’s law in the year 1820. This is a rule or law which helps to calculate the magnitude of the magnetic field due to a current carrying conductor.

Let ‘dl’ be a current element of a conductor ‘XY’ carrying current ‘I’. Let ‘P’ be a point at a distance ‘r’ from ‘dl’, where the magnetic field is to be determined. Let θ be the angle between ‘dl’ and ‘r’.
Now, according to Biot-Savart’s law, the elementary magnetic field ‘dB’ at the point ‘P’ due to current element ‘dl’ is:
i) directly proportional to magnitude of current passing through it, i.e. dB ∝ I …. (i)
ii) directly proportional to the length of current element, i.e. dB ∝ dl …. (ii)
iii) directly proportional to sine angle between ‘dl’ and ‘r’, i.e. dB ∝ sinθ …. (iii)
iv) inversely proportional to square of the distance between ‘dl’ and ‘P’, i.e. dB ∝ 1/r2 …. (iv)

Now, combining the above given relations (i), (ii), (iii) and (iv), we get,
dB ∝ Idlsinθ/r2
∴ dB = kIdlsinθ/r2, where k is proportionality constant.

In S.I. system,
k = μo/, where μo = 4π &times; 10-7 H/m.

In C.G.S. system, k=1. So,
dB = μo/×Idlsinθ/r2 …. (v)

∴ This is the mathematical form of Biot-Savart’s law.

The total magnetic field due to the whole conductor is obtained by integrating the equation (v),

∴ B =∫dB
or, B = ∫μIdlsinθ/4πr2

∴ B = μo/Idlsinθ/r2

There are different theories which help to determine whether a substance is an acid or base. The major and generally accepted theories are given below:

## 1. Arrhenius Theory

According to Arrhenius theory, acid is a chemical substance which gives hydrogen ions only as cation when dissolved in water and base is a chemical substance which gives hydroxide ion only as anion when dissolved in water. Thus, HCl, HNO3, HClO3 are the examples of Arrhenius acid and NaOH, KOH are the examples of Arrhenius base.
Similarly, salt is a chemical substance which gives cation other than hydrogen ion and anion other than hydroxide ion when dissolved in water.
Acid and base react together to give salt and water as:

HCl + NaOH → NaCl + H2

Writing the above chemical equation in ionic form, we get,

H+ + Cl + Na+ + OH → Na+ + Cl + H2O

Eliminating the ions that appear in both sides, we get,

H+ + OH → H2O

Thus, acid base reaction may be defined as the reaction involving combination of H+ ion of acid with OH ion of base forming water molecule.

### Limitations of Arrhenius Theory

• Nature of H+ ion: Aqueous solution of acid does not contain H+ ion. The H+ ion produced by ionization of acid combines with water to form hydronium ion.

H+ + H2 → H3O+

• Limited scope: This theory can predict whether given substance is acidic or basic only when water is taken as solvent.
• Some compounds like AlCl3, BF3, CO2 etc. do not contain hydrogen in their molecular formulae but they act as acid and some compounds like NH3 do not contain -OH in their molecular formulae but they act as base. This fact couldn’t be explained by this theory.
• This theory couldn’t explain about the acidic properties of some cations like Ag+, Cu++ etc. and basic nature of some anions like O, Cl, Cl etc.

## 2. Lowry-Bronsted Theory of Acid and Base

According to this theory, acid is a chemical substance which can donate proton to base and base is a chemical substance which can accept proton from acid. Thus, acid is a proton donor and base is a proton acceptor.

For example,

HCl + NH3 ↔ NH4+ + Cl

In the above reaction, HCl donates a proton to NH3, thus HCl acts as acid and NH3 acts as base.

Similarly,

HCl + H2O ↔ H3O+ + Cl

Here, water gains a proton from HCl and hence acts as base.

H2O + NH3 → NH4+ + OH

In above reaction, water donates a proton to NH3 and hence acts as acid. Since water acts as both acid and base, it is called amphoteric substance. Again, let us consider a reaction,

In the given reaction, acetic acid donates a proton to water in forward reaction. Hence, CH3COOH acts as acid and H2O acts as base. Similarly, in backward reaction, CH3COO accepts a proton from H3O+. Thus, CH3COO acts as base and H3O+ acts as acid. Hence, CH3COOH and CH3COO are called conjugate acid-base pair.

Conjugate acid base pair is the pair of acid and base which can be obtained from each other by just loss or gain of a proton. Similarly, H2O and H3+ are other examples of conjugate acid base pair.

According to Lowry-Bronsted theory, acid-base reaction is the reaction involving formation of corresponding acid-base pair. Further, if an acid is strong, its conjugate base must be weak and vice-versa.

### Limitations of Lowry-Bronsted Theory

Although this theory can predict acidic and basic character of many compounds, it still has some limitations. They are:

• This theory could not explain about acidic nature of AlCl3, BF3 and CO2.
• It could not explain about acidic nature of some metal ions like Ca++, Ag+ etc. and basic characters of some anions like O, Cl etc.

## 3. Lewis Theory of Acid and Base

Lewis theory of acid and base is based on negative charge and according to this theory, acid is a chemical substance which can accept lone pair of electrons and base is a chemical substance which can donate lone pair of electrons to acid. Thus, acid is acceptor of lone pair of electron and base is the donor of lone pair of electrons.

Let us consider a reaction,

In above reaction, lone pair of electrons are donated by ammonia by H+ ion. Thus, ammonia acts as Lewis base and H+ ion acts as Lewis acid.
Similarly,

In the above reaction, BF3 accepts a lone pair of electrons from ammonia and hence acts as acid.
According to Lewis theory, acid-base reaction is the reaction involving the formation of coordinate covalent bond between acid and base.

### Limitations of Lewis Theory

According to Lewis theory, acid-base reaction is the reaction which involves the formation of coordinate covalent bond between acid and base. The formation of coordinate covalent bond is a slow reaction but acid-base reaction is fast reaction. Thus, this fact couldn’t be explained by Lewis theory.