Moving Charges And Magnetism Class 12 Notes Physics Chapter 4 - CBSE

Chapter : 4

What are Moving Charges And Magnetism ?

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Concept Of Magnetic Field

Magnetic field is a region or space around a magnet or a current carrying conductor or a moving charge, in which its magnetic effect can be felt.

Magnetic field is a vector quantity.
SI unit of magnetic field is tesla (T).

Oersted’s Experiment

Oersted’s experiment verified that a current carrying conductor produces a magnetic field around it and this magnetic field can be detected by bringing a magnetic needle in the vicinity of the current carrying conductor.
The strength and the direction of the magnetic field depend on the magnitude and direction of the current.

Biot-savart Law

$$\text{Biot-Savart law states that magnitude of intensity of small magnetic field} \space\vec{\text{dB}}\space \text{due to current I carrying current element} \space\vec{\text{dl}}\space \text{at any point P at distance r from it is given by}$$

$$|\text{d}\vec{\text{B}}|=\frac{\mu_0}{4\pi}.\frac{\text{I}_1|\vec{\text{dl}}×\vec{\text{r}}|}{\text{r}^3}$$

$$\text{where} \space\theta \space \text{is the angle between r and} \space\vec{\text{dl}} \space\text{and} \space\mu_0 = 4\pi × 10^{-7} \text{Tm \space A}^{-1}\space \text{is called permittivity of free space.}$$

Application Of Biot-savart Law TO Current Carrying Circular Loop

Magnetic field at the centre of a circular current carrying coil of radius a is B =(µ₀/4π).(2πI/a)=(µ₀I/2a)
Magnetic field at a point on the axis of the circular current carrying coil of radius a is B =(µ₀/4π).(2πIa²/(a²+r²)^3/2)

Ampere’s Law

$$\oint\vec{\text{B}}.\vec{\text{dl}}=\mu_0\text{I}$$

Ampere’s circuital law is analogous to Gauss law in electrostatics.

Application Of Ampere’s Law To Infinitely Long Straight Wire

Magnetic field due to an infinitely long straight solid cylindrical wire of radius a and carrying current I.
Magnetic field at a point outside the wire i.e., (r > a), is B =(µ₀I/2πr)
Magnetic field at a point inside the wire i.e., (r < a), is B =(µ₀Ir/2πa²)
Magnetic field at a point on the surface of the wire i.e., (r = a), is B =(µ₀Ir/2πa)

Force On A Moving Charge In Uniform Magnetic And Electric Fields

Force observed by Lorentz in electric and magnetic field on a moving charge is given by,

$$\vec{\text{F}}=\text{q}(\vec{\text{E}}+\vec{\text{V}}+\vec{\text{B}})=\vec{\text{F}}_\text{e}+\vec{\text{F}}_\text{m}$$

$$\text{where}\space\vec{\text{F}_\text{e}}\space\text{is the electric force,}\space\vec{\text{F}}_\text{m}$$

is the magnetic force and v is the velocity with which the charge is moving.

Force On A Current Carrying Conductor In A Uniform Magnetic Field

Force experienced by a straight conductor of length l carrying current I when placed in a uniform magnetic

$$\text{field B is,}\space\vec{\text{F}}=\text{I}(\vec{\text{l}}×\vec{\text{B}})=\text{BIl sin}\space\theta$$

where θ is the angle between l and B.

Direction of this force is given by Fleming’s left hand rule.

Force Between Two Parallel Current Carrying Conductors Definition Of Ampere

When two parallel conductors separated by a distance r carry currents I₁ and I₂, the magnetic field of one

will exert a force on the other. The force per unit length on either conductor is F =(µ₀/4π)(2I₁I₂/r)

It gives definition of one ampere and force experienced by each wire in this case is 2 × 10⁷ N m^-1.

Parallel currents attract and antiparallel currents repel.

Torque Experienced By A Current Loop In Uniform Magnetic Field

Torque on a coil of area A, having n turns, carrying current I, when suspended in a magnetic field of strength B is given by τ = nIBA sin θ where θ is the angle which a normal drawn on the plane of the coil makes with the direction of magnetic field.

Moving Coil Galvanometer

It is an instrument used for the detection and measurement of small currents.
It is based on the principle that, when a current carrying coil is placed in magnetic field, it experiences a torque.
where G =(K/NAB)=galvnometer constant

A = area of the coil

N = number of turns in the coil

B = strength of magnetic field

K = torsional constant of the spring i.e., restoring torque per unit twist.

Current Sensitivity Of A Galvanometer

It is defined as the deflection produced in the galvanometer, when unit current flow through it.

Is =(θ/I)=(NAB/k)

The unit of current sensitivity is rad A^-1 or div A^-1.

Conversion Of Galvanometer Into An Ammeter

A galvanometer can be converted into an ammeter of given range by connecting a suitable low resistance S called shunt in parallel to the given galvanometer, whose value is given by S =(I_g/I-I_g)G
where I_g is the current for full scale deflection of galvanometer, I is the current to be measured by the galvanometer and G is the resistance of galvanometer.
Voltmeter is a high resistance instrument and is always connected in parallel with the circuit element across which potential difference is to be measured.
An ideal voltmeter has infinite resistance.

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