4.6 Magnetic Field on the Axis of Circular Current Loop

Subject: Physics

Class : XII

Chapter 4. Moving Charges and Magnetism

4.6 Magnetic Field on the Axis of Circular Current Loop

Consider about a circular loop of radius R carrying the current I. The loop is placed in the y-z plane with its centre at the origin O. The x axis is the axis of the loop. There is a point P at a distance x from the centre of the loop at which magnetic field is to be determined.

Mathematical Calculation

dl is the conducting element of the loop.

The magnitude of dB of the magnetic field due to dl is according to Biot-Savart Law

dB = 𝝁₀I|dlxr|/4𝜋r³
Now 
r² = x² + R²
Any element to loop will be perpendicular to the displacement vector r from dl to the axial point P is in the x-y plane.
Hence,
|dlxr| = rdl
∴dB = 𝝁₀Idlr/4𝜋r³ ............... (i)
Now putting the value of r
dB = 𝝁₀Idl/4𝜋(x² + R²)
The direction of dB is perpendicular to the plane formed by dl and r.
It has an x- component dBₓ and a component perpendicular to x-axis dB⫡.
When the components perpendicular to the x- axis are summed over, they cancel out.
Only the x component survives.
∴dBₓ = dBcos𝜃
From figure 
cos𝜃 = R/√(x² + R²) ............. (ii)
Now from eqn. no. (i) and (ii)
dBₓ = 𝝁₀IdlR/4𝜋(x² + R²)³/²
For whole circular loop
dl = 2𝜋R
Magnetic field at P due to entire circular loop
= B = Bₓi = 𝝁₀IR²/2𝜋(x² + R²)³/²i
Field at the centre of the loop. Here x = 0
B₀ = 𝝁₀I/2R

The direction of the magnetic field is determined by the help of 
Fleming Right Hand Thumb rule.

11. Alcohols, Phenols and Ethers

Alcohols, Phenols and Ethers

Class XII

Subject : Chemistry

Alcohols

Alcohols are compounds in which a hydroxyl(-OH) group attached to the saturated carbon atom.

General formula of alcohol - R-OH

The hydroxyl group is the functional group of alcohols.

Alcohols containing one hydroxyl are called Monohydric Alcohols.

Alcohols with two, three, or more hydroxyl groups are known as Dihydric Alcohols, Trihydric Alcohols, and Polyhydric Alcohols respectively.

For example,

Primary, Secondary and Tertiary Alcohols

Monohydric alcohols are classified as primary, secondary or tertiary depending upon whether the -OH group is attached to primary, secondary or a tertiary carbon.

Structure

Consider about the structure of Methyl Alcohol (CH₃OH). In methyl alcohol both oxygen and carbon are sp³ hybridized. Two of the sp³ orbitals of oxygen are completely filled and cannot take part in bond formation.

The C-O bond methyl alcohol is formed by overlap of an sp³ orbital of carbon and an sp³ orbital of oxygen. The O-H bond is formed by overlap of an sp³ orbital of oxygen and s orbital of hydrogen. The C-O-H bond angle is 105⁰. It is less than the normal tetrahedral angle. This is because the two completely filled sp³ orbitals of oxygen repel each other. This result in reduction of the bond angle.

Structure of Methyl Alcohol is given below

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