1) Ohms Law
The statement of Ohm’s law
If potential difference or voltage is applied across a resistor of a closed circuit, current starts flowing through it.
This current is directly proportional to the voltage applied if temperature and all other factors remain constant. Thus we can mathematically express it as:
This equation show statement of ohms law.
where,
I= is the current through the resistor measured in Ampere (Ampere, or amps),
V=the Voltage/potential difference applied across the resistor in unit of volt,
R=ohm(Ω) is the unit of measure for the resistance of the resistor R
It’s important to note that the resistance R is the property of the conductor and theoretically has no dependence on the voltage applied, or on the flow of current. The value of R changes only if the conditions (like temperature, diameter length etc.) of the material are changed by any means.
Resistivity of each material is different it depend on material not on the applied voltage and current.
Easy to remember
3) Faraday's Law of Electromagnetic Induction
Method to change magnetic field:
Consider a magnet approaching towards a coil. Here we consider two instants at time T1 and time T2. Flux linkage with the coil at time, T1 = NΦ1 Wb Flux linkage with the coil at time, T2 = NΦ2 wb Change in flux linkage = N(Φ2 - Φ1) Let this change in flux linkage be, Φ = Φ2 - Φ1 So, the Change in flux linkage = NΦ Now the rate of change of flux linkage = NΦ / t Take derivative on right hand side we will get The rate of change of flux linkage = NdΦ/dt But according to Faraday's law of electromagnetic induction, the rate of change of flux linkage is equal to induced emf.
Considering Len'z Law
Where, flux Φ in Wb = B.A
B = magnetic field strength
A = area of the coil
HOW TO INCREASE EMF INDUCED IN A COIL
Hold out your left hand with forefinger, second finger and thumb at right angle to one another. If the fore finger represents the direction of the field and the second finger that of the current, then thumb gives the direction of the force. While, current flows through a conductor, one magnetic field is induced around it. This can be imagined by considering numbers of closed magnetic lines of force around the conductor. The direction of magnetic lines of force can be determined by Maxwell's corkscrew rule or right-hand grip rule. As per these rules, the direction of the magnetic lines of force (or flux lines) is clockwise if the current is flowing away from the viewer, that is if the direction of current through the conductor is inward from the reference plane as shown in the figure.
Now if a horizontal magnetic field is applied externally to the conductor, these two magnetic fields i.e. field around the conductor due to current through it and the externally applied field will interact with each other. We observe in the picture, that the magnetic lines of force of external magnetic field are from N to S pole that is from left to right. The magnetic lines of force of external magnetic field and magnetic lines of force due to current in the conductor are in same direction above the conductor, and they are in opposite direction below the conductor. Hence there will be larger numbers of co-directional magnetic lines of force above the conductor than that of below the conductor. Consequently, there will be a larger concentration of magnetic lines of force in a small space above the conductor. As magnetic lines of force are no longer straight lines, they are under tension like stretched rubber bands. As a result, there will be a force which will tend to move the conductor from more concentrated magnetic field to less concentrated magnetic field, that is from present position to downwards. Now if you observe the direction of current, force and magnetic field in the above explanation, you will find that the directions are according to the Fleming left hand rule.
5) Fleming Right Hand Rule
As per Faradays law of electromagnetic induction, whenever a conductor moves inside a magnetic field, there will be an induced current it. If this conductor gets forcefully moved inside the magnetic field, there will be a relation between the direction of applied force, magnetic field and the current. This relation among these three directions is determined by Fleming Right Hand Rule This rule states "Hold out the right hand with the first finger, second finger and thumb at right angle to each other. If forefinger represents the direction of the line of force, the thumb points in the direction of motion or applied force, then second finger points in the direction of the induced current.
5) Gauss Law
There is always Static electric field around positive and negative charge Actually this flux is radiated/from the electric charge. Now amount of this flow of flux depends upon the quantity of charge it is emanating from. To find out this relation, the Gauss's theorem was introduced. This theorem can be considered as one of the most powerful and most useful theorem in the field of electrical science. We can find out the amount of flux radiated through the surface area surrounding the charge from this theorem.This theorem states that the total electric flux through any closed surface surrounding a charge, is equal to the net positive charge enclosed by that surface. Suppose the charges Q1, Q2_ _ _ _Qi, _ _ _ Qn are enclosed by a surface, then the theorem may be expressed mathematically by surface integral as
Where, D= is the flux density in coulombs/m2
dS= is the outwardly directed vector.
For better explanation lets go through example consider Q be the charge at the center and charge is normal to the subsurface states that total charge emanated from body equal to charge Q coulombs if charge is not place at the center other than center
This is the integral form of Gauss's theorem. And hence this theorem is proved.
The statement of Ohm’s law
If potential difference or voltage is applied across a resistor of a closed circuit, current starts flowing through it.
Now putting the constant of proportionality we get,
where,
I= is the current through the resistor measured in Ampere (Ampere, or amps),
V=the Voltage/potential difference applied across the resistor in unit of volt,
R=ohm(Ω) is the unit of measure for the resistance of the resistor R
It’s important to note that the resistance R is the property of the conductor and theoretically has no dependence on the voltage applied, or on the flow of current. The value of R changes only if the conditions (like temperature, diameter length etc.) of the material are changed by any means.
Resistivity of each material is different it depend on material not on the applied voltage and current.
Easy to remember
3) Faraday's Law of Electromagnetic Induction
Faraday's First Law
Any change in the magnetic field of a coil of wire will cause an emf to be induced in the coil. This emf induced is called induced emf and if the Conductor circuit is closed, the Current will also circulate through the circuit and this current is called induced current.
Method to change magnetic field:
- By moving a magnet towards or away from the coil
- By moving the coil into or out of the magnetic field.
- By changing the area of a coil placed in the magnetic field
- By rotating the coil relative to the magnet
Faraday's Second Law
It states that the magnitude of emf induced in the coil is equal to the rate of change of flux that linkages with the coil. The flux linkage of the coil is the product of number of turns in the coil and flux associated with the coil.Faraday Law Formula
Consider a magnet approaching towards a coil. Here we consider two instants at time T1 and time T2. Flux linkage with the coil at time, T1 = NΦ1 Wb Flux linkage with the coil at time, T2 = NΦ2 wb Change in flux linkage = N(Φ2 - Φ1) Let this change in flux linkage be, Φ = Φ2 - Φ1 So, the Change in flux linkage = NΦ Now the rate of change of flux linkage = NΦ / t Take derivative on right hand side we will get The rate of change of flux linkage = NdΦ/dt But according to Faraday's law of electromagnetic induction, the rate of change of flux linkage is equal to induced emf.
Considering Len'z Law
HOW TO INCREASE EMF INDUCED IN A COIL
- By increasing the number of turns in the coil i.e N- From the formulae derived above it is easily seen that if number of turns of coil is increased, the induced emf also gets increased.
- By increasing magnetic field strength i.e B surrounding the coil- Mathematically if magnetic field increases, flux increases and if flux increases emf induced will also get increased. Theoretically, if the coil is passed through a stronger magnetic field, there will be more lines of force for coil to cut and hence there will be more emf induced.
- By increasing the speed of the relative motion between the coil and the magnet - If the relative speed between the coil and magnet is increased from its previous value, the coil will cut the lines of flux at a faster rate, so more induced emf would be produced.
Applictions: Transformer,generator,Induction cookers Etc.
4) Lenz law:
Lenz's law states that when an emf is generated by a change in Magnetic Flux according to Faraday's Law, the polarity of the induced emf is such, that it produces an Current that's magnetic field opposes the change which produces it.
The negative sign used in Faraday's law of electomagnetic induction indicates that the induced emf ( ε ) and the change in magnetic flux ( δΦB ) have opposite signs.
Where,
ε = Induced emf
δΦB = change in magnetic flux
N = No of turns in coil
Reason for Opposing, Cause of Induced Current in Lenz's Law?
- As stated above, Lenz's law obeys the law of conservation of energy and if the direction of the magnetic field that creates the current and the magnetic field of the current in a conductor are in same direction, then these two magnetic fields would add up and produce the current of twice the magnitude and this would in turn create more magnetic field, which will cause more current and this process continuing on and on leads to violation of the law of conservation of energy.
- If the induced current creates a magnetic field which is equal and opposite to the direction of magnetic field that creates it, then only it can resist the change in the magnetic field in the area, which is in accordance to the Newton's third law of motion.
4) Fleming Left Hand Rule
It is found that whenever an current carrying conductor is placed inside a magnetic field, a force acts on the conductor, in a direction perpendicular to both the directions of the current and the magnetic field. In the figure it is shown that, a portion of a conductor of length L placed vertically in a uniform horizontal magnetic field strength H, produced by two magnetic poles N and S. If i is the current flowing through this conductor, the magnitude of the force acts on the conductor is,
F = BiL 
5) Fleming Right Hand Rule
As per Faradays law of electromagnetic induction, whenever a conductor moves inside a magnetic field, there will be an induced current it. If this conductor gets forcefully moved inside the magnetic field, there will be a relation between the direction of applied force, magnetic field and the current. This relation among these three directions is determined by Fleming Right Hand Rule This rule states "Hold out the right hand with the first finger, second finger and thumb at right angle to each other. If forefinger represents the direction of the line of force, the thumb points in the direction of motion or applied force, then second finger points in the direction of the induced current.
5) Gauss Law
There is always Static electric field around positive and negative charge Actually this flux is radiated/from the electric charge. Now amount of this flow of flux depends upon the quantity of charge it is emanating from. To find out this relation, the Gauss's theorem was introduced. This theorem can be considered as one of the most powerful and most useful theorem in the field of electrical science. We can find out the amount of flux radiated through the surface area surrounding the charge from this theorem.This theorem states that the total electric flux through any closed surface surrounding a charge, is equal to the net positive charge enclosed by that surface. Suppose the charges Q1, Q2_ _ _ _Qi, _ _ _ Qn are enclosed by a surface, then the theorem may be expressed mathematically by surface integral as
Where, D= is the flux density in coulombs/m2
dS= is the outwardly directed vector.
For better explanation lets go through example consider Q be the charge at the center and charge is normal to the subsurface states that total charge emanated from body equal to charge Q coulombs if charge is not place at the center other than center
At that time, the flux lines are not normal to the surface surrounding the charge, then this flux is resolved into two components which are perpendicular to each other, the horizontal one is the sinθ component and the vertical one is the cosθ component. Now when the sum of these components is taken for all the charges, then the net result is equal to the total charge of the system which proves Gauss's theorem.
Proof of Gauss’s Theorem
Let us consider a point charge Q located in a homogeneous isotropic medium of permittivity ε.
The Electric field intensity at any point at a distance r from the charge is
The flex density is given as,
Now from the figure the flux through area dS
Where, θ is the angle between D and the normal to dS
Now, dScosθ is the projection of dS is normal to the radius vector.
By definition of a solid angle
Where, dΩ is the solid angle subtended at Q by the elementary surface are dS. So the total displacement of flux through the entire surface area is
By definition of a solid angle
Now, we know that the solid angle subtended by any closed surface is 4π steradians, so the total Electric Flux through the entire surface is
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