CBSE Class 12th Physics Notes: Moving Charges and Magnetism (Part ‒ III)

CBSE class 12 Physics chapter wise notes on Chapter-4: Moving Charges and Magnetism of NCERT class 12 Physics textbook are available in this article.

This article is a continuation of the revision notes on Moving Charges and Magnetism, Part ‒ I and Part – II. In previous parts, we have studied important topics like, Magnetic field due to a current element, Biot-Savart Law, Ampere’s Circuital Law, magnetic field due to a solenoid and a toroid, Oersted’ experiment, moving charge & magnetic field, Lorentz Force, magnetic force on a current-carrying conductor, motion of a charged particle in a magnetic Field, Cyclotron etc.

In this part we will study some more important topics which are given below:

• Force between two Parallel Current Carrying Wires
• Definition of Ampere
• Torque on a Rectangular Current loop in a Uniform Magnetic Field
• Magnetic Dipole Moment of a Revolving Electron
• Potential Energy of a current loop in a Magnetic Field
• Moving Coil Galvanometer
• Sensitivity of a Galvanometer
• Conversion of a Galvanometer into Voltmeter
• Conversion of a Galvanometer into Ammeter

The notes are as follows:

Force between two Parallel Current Carrying Wires

Image Source: NCERT textbooks

Two long parallel conductors a and b kept at a distance d apart in vaccum and carrying a current I_a and I_b respectively. The force per unit length experienced by each of them is given by

This force will be equal and opposite on both wires.

Nature of force of interaction between the current carrying conductors can be explained on the basis of Fleming’s left hand rule.

In general, two long parallel conductors carrying current

• in same direction will attract each other
• in different direction will repel each other

Definition of Ampere

Definition of ampere follows from the formula for force between two parallel current carrying conductors.

When 1 ampere each is passing through two long, parallel conductors kept 1 m apart in vacuum, a force of magnitude 2 × 10^‒7 N is experienced by a meter length of each conductor.

Torque on a Rectangular Current loop in a Uniform Magnetic Field

A rectangular loop having N turns of area A each, carrying a steady current I and placed in a uniform magnetic field B such that the normal to the plane of the loop makes an angle θ with the direction of the magnetic field B, then a torque τ experienced by the loop whose magnitude is given by, τ = NIAB sinθ.

This equation can be expressed in vector form as shown below:

Here, |m| = NIA is called magnetic dipole moment of the current loop.

One can define magnetic dipole moment of the current carrying loop as product of current in the loop and total area of the loop, i.e., M = I (NA).

Magnetic dipole moment is a vector quantity and its direction is along the direction of magnetic field due to the current in the loop. We can also find the direction of dipole moment vector with the help of right hand grip rule.

Magnetic Dipole Moment of a Revolving Electron

Any charge in uniform circular motion would have an associated magnetic moment given by,

Here, e = 1.6 × 10^‒19 C, m_e = 9.1 × 10^‒31 kg, l is the magnitude of the angular momentum of the electron about the central nucleus (“orbital” angular momentum) and |l| = (n h)/2π, where, n is a natural number (n = 1, 2, 3, ....) and h is a constant named after Max Planck (Planck’s constant) with a value h = 6.626 × 10^–34 J s.

The negative sign indicates that the angular momentum of the electron is opposite in direction to the magnetic moment. Instead of electron with charge (– e), if we had taken a particle with charge (+ q), the angular momentum and magnetic moment would be in the same direction.

CBSE Class 12 NCERT Solutions

Potential Energy of a current loop in a Magnetic Field

If a current loop of magnetic moment, M = NIA is held in a uniform magnetic field B in such a way that direction of magnetic dipole moment makes an angle θ with the direction of magnetic field, then the potential energy of the dipole is given by,

Moving Coil Galvanometer

It is an instrument used for detection and measurement of small current.

The galvanometer consists of a light rectangular coil of N turns each having area A wound on an aluminium frame.

The coil is free to rotate free to rotate about a fixed axis (as shown in figure given below), in a uniform radial magnetic field.

Image Source: NCERT textbooks

There is a cylindrical soft iron core which is used to make the field radial and also to increase the strength of the magnetic field.

When a current flows through the coil, a torque acts on it. This torque is given by, τ = NIAB where the symbols have their usual meaning.

Since the field is radial by design, we have taken sin θ = 1 in the above expression for the torque. The magnetic torque NIAB tends to rotate the coil. A spring S_p provides a counter torque kϕ that balances the magnetic torque NIAB; resulting in a steady angular deflection ϕ. In equilibrium

kϕ = NI AB

Here, k is the torsional constant of the spring; i.e. the restoring torque per unit twist.

The deflection ϕ is indicated on the scale by a pointer attached to the spring. We have

The quantity in brackets is a constant for a given galvanometer.

Sensitivity of a Galvanometer

Current Sensitivity:

Current sensitivity of a galvanometer is defined as the deflection per unit current

Mathematically,

Voltage Sensitivity:

Voltage sensitivity of a galvanometer is defined as the deflection per as the deflection per unit voltage.

Mathematically,

Conversion of a Galvanometer into Voltmeter

Image Source: NCERT textbooks

A galvanometer of coil resistance R_G, showing full scale deflection for a current I_G can be converted into a voltmeter for measuring potential differences having values greater than I_GR_G by connecting high resistance R in series with the galvanometer where,

An ideal voltmeter has infinite resistance.

Conversion of a Galvanometer into Ammeter:

Image Source: NCERT textbooks

A galvanometer of coil resistance R_G, showing full scale deflection for a current I_G can be converted into an ammeter for measuring current having values more than I_G (i.e., I > I_G) by putting a low resistance r_S in parallel with the galvanometer where,

Here, r_s is also called shunt resistance. An ideal ammeter has zero resistance.