Chapter : 4

What are Moving Charges And Magnetism ?

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

biotsavartlaw

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

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

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

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 =(Ig/I-Ig)G
  • where Ig 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.