Electricity and Magnetism

Electricity and Magnetism,

Two seemingly different topics ( atleast till grade 9) are actually just two different faces of a coin, one is related to the other, one instigates the other.

Taught to high schoolers in vast detail, it carries as much importance in our report cards as it does in our real life ( Now, imagine living your life without TV or your laptop , these devices use both magnetism and electricity! That is the percentage of importance it plays in our report cards too ( *gulp*))

Hence, in this blog we will go through the important formulas, units and concepts in these chapters

So, let's start!

Important units and formulas

1) Electric charge -- Coloumb

-- CGS Unit - Electrostatic unit (esu) ( 1 Coloumb = 3 * 10⁹ esu)

-- Faraday ( 1F = 96500C)

-- Ampere - hour ( 1 A-hr = 3600 C)

2) Electric filed intensity - The force acting on a unit positive charge, place at a point within the electric field, is called electric field intensity at that point

-- Newton / Coloumb

-- Volt/Meter

-- Vector quantity

3) Electric Potential - Work done per unit positive charge to move from one point to another

-- Volt

-- V = Work done / charge

-- Scalar quantity

4) Electric current - The rate of flow of electric charge through any cross section

-- Ampere

-- I = charge that flows across / time

-- Scalar quantity

5) Electrical Resistance - The property of a material which offers opposition to the electric current and dissipates energy

-- Ohm

-- R = Volt / Ampere

6) Resisitivity - The characteristic property to resist the electricity flowing through it

-- Ohm meter

7) Conductance - A measure of ease to the flow of current in the circuit

-- (ohm) ⁻¹ , mho , siemens

8) Conductivity - The characteristic property to allow the electricity to flowing through it

-- (ohm -m )⁻¹ , mho m⁻¹ , siemens m⁻¹

9) Electric power - The work done per unit time by a source in order to maintain electric current in a circuit is called ' electric power'

-- Watt

-- Watt = Volt * Ampere or Volt ² / Resistance or Current ² * Resistance

10) Electric energy - The total energy supplied by a source in order to maintain the electric current in the circuit in a given time

-- Joule

-- E = Volt * Ampere * Time

11) Magnetic Field Induction/ Magnetic flux density -- Tesla

-- CGS unit -- Gauss ( 1Gauss = 10⁻⁴ Tesla)

Coulomb's Law

The force of attraction or repulsion between two point charges at rest is directly proportional to the product of the charges and inversely proportional to the square of the distance between them and it always acts along the line joining the charges

F ∝ Q1 * Q2

F ∝ 1 / r ²

F ∝ Q1 Q2 / r²

F = K * Q1* Q2 / r² ( K is the constant of proportionality)

Newton vs Coloumb 😂

Magnitude of Magnetic field

A) An infinitely long conductor

The magnitude of manetic field produced by an infinitely long conductor ( when no exact measurement is given hence is considered infinitely long on both ends) in a vacuum at a distance r from it, is given by

where,

B = Magnetic field strength

μ = Permeability of vacuum ( a constant)

I = current flowing in a conductor

r = distance from the conductor ( where magnetic field is measured)

B) Semi-infinite long conductor

The magnitude of manetic field produced by a semi -infinitely long conductor ( semi - infinitely is one of the ends has an specified stop while the other is considered infinitely long) in a vacuum at a distance r from it, is given by

where, B = Magnetic field strength μ = Permeability of vacuum ( a constant) I = current flowing in a conductor r = distance from the conductor ( where magnetic field is measured) C) Circular wire The magnitude of magnetic field at centre produced by current carrying circular conducting wire

where, B = Magnetic field strength N = number of turns μ = Permeability of vacuum ( a constant) I = current flowing in a conductor r = radius of coil Lorenz Force I) A electric current flowing through a conductor produces a magnetic field , the field so produced exerts a force on a magnet placed in the vicinity of the condutor, hence the magnet must also exert an equal and opposit force on the current- carrying conductor (And here we thought we were done with Newton and his laws in 9th itself! 😅) The measure of this force can be given by the formula F = qVB sin Ө where, q = charge v = velocity B = magnetic field Ө = angle between V and B * The force is considered to be maximum when all the forces act perpendicular as :- sin 90⁰ = 1 hence qVB = F max * Force is zero , 1) If the charge is stationary ( V= 0) 2) If the charge is moving in the direction of magnetic field ( sin 0⁰ = 0 ) 3) If the charge is moving in the direction opposite to magnetic field (sin 180⁰ = 0 ) II) On a conductor F = BI ℓ sinӨ where, I = Current through the conductor B = magnetic field Ө = angle between I and B ℓ = length of the conductor Lenz Law When there is a fluctuation or change in the magnetic field influencing an electric circuit, current is induced, and the direction ( or polarity) of the current induced is said to always oppose the cause. CASE 1 = If the north pole moves towards the coil - Coil gets induced North pole ( here, the cause is moving of north pole towards the coil hence to oppose this, the coil induces North pole to repel ( or push away) CASE 2 = If the north pole moves away coil - Coil gets induced South pole ( here, the cause is moving the north pole away from the coil hence to oppose this, the coil induces South pole to attract ( or pull) CASE 3 = When south pole moves towards the coil - coil gets induced south pole CASE 4 =When south pole ,oves away from the coil - coil gets north induced Relation between Resistance and Power ( Brightness) a) If we compare two resistances connected to separate circuits - More the resistance , less the power ( brightness ) - Less the resistance , more the power b) If we compare the resistances connected in series - More the resistance, more the power c) If we compare the resistance connected in parallel - Less the resistance , more the power And more the power -- less the current drawn