Magnetic Effects of Current & Magnetism – Class XII Physics
Magnetic Effects of Current
& Magnetism
Exploring the fascinating relationship between electricity and magnetism, and understanding the behavior of magnetic materials.
Topics We’ll Cover:
Moving Charges and Magnetism
Magnetic Field and Field Lines
Biot-Savart Law
Ampere’s Circuital Law
Earth’s Magnetism
Magnetic Properties of Materials
Page 1 of 18
Historical Background: Oersted’s Experiment
The Accidental Discovery (1820)
Hans Christian Oersted discovered the connection between electricity and magnetism during a physics lecture at the University of Copenhagen.
The Experiment
Oersted noticed that a compass needle deflected when an electric current flowed through a nearby wire.
- Before current: compass needle aligned with Earth’s magnetic field
- During current flow: compass needle deflected perpendicular to the wire
- Reversing current: needle deflected in the opposite direction
Significance of the Discovery
First evidence that electricity and magnetism are related phenomena
Led to the development of electromagnetic theory
Foundation for technologies like electric motors, generators, and transformers
Page 2 of 18
Concept of Magnetic Field
Definition
The magnetic field is a region around a magnetic material or a moving electric charge within which the force of magnetism acts.
SI Unit: Tesla (T) or Weber per square meter (Wb/m²)
CGS Unit: Gauss (G), where 1 Tesla = 10,000 Gauss
Properties of Magnetic Field Lines
- Magnetic field lines form continuous closed loops
- They originate from north pole and terminate at south pole outside the magnet
- Field lines never intersect each other
- The tangent to a field line at any point represents the direction of the magnetic field at that point
- The density of field lines indicates the strength of the magnetic field
Magnetic Field Lines of a Bar Magnet
Mathematical Representation
The magnetic force experienced by a charge q moving with velocity v in a magnetic field B is given by:
The direction is determined by the right-hand rule for cross products.
Page 3 of 18
Biot-Savart Law
Definition
The Biot-Savart law relates the magnetic field generated by an electric current to the magnitude, direction, length, and proximity of the electric current.
Mathematical Expression
dB = μ0 / 4π · Idl × r̂ / r2
For a current element Idl at position r
Key Parameters
- dB – Magnetic field produced at point P
- μ0 – Permeability of free space (4π × 10-7 T·m/A)
- I – Current flowing through the conductor
- dl – Infinitesimal length of the current element
- r – Distance from the current element to point P
- r̂ – Unit vector from the current element to point P
Biot-Savart Law Visualization
Applications
-
Magnetic field due to a straight conductor:
B = (μ₀I/2πr) for an infinitely long straight wire
-
Magnetic field at the center of a circular loop:
B = (μ₀I/2R) for a circular loop of radius R
-
Magnetic field due to a solenoid:
B = μ₀nI where n is the number of turns per unit length
-
Design of electromagnets and electromagnetic devices
Important Notes
The direction of the magnetic field is perpendicular to both dl and r (determined by right-hand rule)
The total magnetic field at a point is the vector sum of the contributions from all current elements
Page 4 of 18
Ampere’s Circuital Law
Definition
Ampere’s Circuital Law relates the integrated magnetic field around a closed loop to the electric current passing through the loop.
Mathematical Expression
∮ B · dl = μ0 Ienc
Where Ienc is the total current enclosed by the loop
Key Elements
- ∮ – Line integral around a closed loop
- B – Magnetic field
- dl – Infinitesimal length element along the loop
- μ0 – Permeability of free space (4π × 10-7 T·m/A)
- Ienc – Current enclosed by the Amperian loop
Ampere’s Law Visualization
Applications
Infinite Straight Wire
B = μ₀I / 2πr
Solenoid
B = μ₀nI
Toroid
B = μ₀NI / 2πr
Outside Conductors
∮ B·dl = 0
Comparison with Biot-Savart Law
Ampere’s Law: More useful when there is symmetry in the current distribution (straight wires, solenoids, toroids)
Biot-Savart Law: More general, applicable to any current-carrying conductor regardless of symmetry
Page 5 of 18
Force on a Moving Charge in a Magnetic Field
Lorentz Force
When a charged particle moves through a magnetic field, it experiences a force perpendicular to both its velocity and the magnetic field.
Mathematical Expression
⃗F = q(⃗v × ⃗B)
|F| = |q|vB sin θ
Where θ is the angle between velocity and magnetic field
Key Points
- Force is maximum when velocity is perpendicular to the magnetic field (θ = 90°)
- Force is zero when velocity is parallel to the magnetic field (θ = 0° or 180°)
- The force changes direction if the charge sign changes
- Direction determined using right-hand rule (for positive charge)
Direction of Force
Motion in a Uniform Magnetic Field
Circular Motion
When v ⊥ B, charged particles move in circular path
Radius: r = mv/|q|B
Period: T = 2πm/|q|B
Helical Motion
When v has components both ⊥ and ∥ to B
Pitch: p = 2πmv∥/|q|B
Radius: r = mv⊥/|q|B
Applications
Mass Spectrometer
Separates ions based on their mass-to-charge ratio using magnetic fields
Cyclotron
Accelerates charged particles in a spiral path to achieve high energies
Cathode Ray Tube
Used in old TVs and oscilloscopes to control electron beam direction
Page 6 of 18
Force on Current-Carrying Conductors
Basic Principle
When a current-carrying conductor is placed in a magnetic field, it experiences a force perpendicular to both the direction of current and magnetic field.
Mathematical Expression
⃗F = I(⃗L × ⃗B)
|F| = ILB sin θ
Where θ is the angle between the current direction and magnetic field
Fleming’s Left-Hand Rule
Used to determine the direction of force:
- First finger points in the direction of magnetic Field
- SeCond finger points in the direction of Current
- Thumb points in the direction of Thrust or force
Force on a Straight Conductor
Applications
DC Motor
Converts electrical energy to mechanical energy
Moving Coil Galvanometer
Measures small electric currents
Force Between Parallel Current-Carrying Conductors
Parallel Currents: Attract each other
Anti-parallel Currents: Repel each other
Force per unit length: F/L = (μ₀/2π) · (I₁I₂/r)
SI Unit of Current
The ampere (A) is defined using the force between two parallel conductors:
1 ampere produces a force of 2×10⁻⁷ N/m between two parallel wires 1m apart
Page 7 of 18
Torque on Current Loops
Basic Principle
When a current-carrying loop is placed in a magnetic field, it experiences a torque that tends to rotate the loop to align its magnetic moment with the field.
Mathematical Expression
⃗τ = ⃗m × ⃗B
|τ| = mB sin θ
Where θ is the angle between the magnetic moment and magnetic field
Magnetic Moment of a Current Loop
- Magnetic moment: ⃗m = IA⃗n
- I = Current in the loop
- A = Area of the loop
- ⃗n = Unit vector normal to the plane of the loop
- Direction given by right-hand rule: curl fingers in direction of current, thumb gives ⃗m direction
Torque on a Current Loop
Potential Energy
A current loop in a magnetic field possesses potential energy due to its orientation:
U = -⃗m · ⃗B = -mB cos θ
Stable Equilibrium
θ = 0° (m parallel to B)
Minimum energy
Unstable Equilibrium
θ = 180° (m anti-parallel to B)
Maximum energy
Applications
Electric Motors
The torque on current loops is the working principle behind electric motors
Galvanometers
Used in measuring instruments where the torque rotates a pointer proportional to current
Loudspeakers
Use torque on a current-carrying coil to move a diaphragm and produce sound
Page 8 of 18
Moving Coil Galvanometer
Principle and Construction
A moving coil galvanometer works on the principle that a current-carrying coil placed in a magnetic field experiences a torque. It converts small electric currents into mechanical deflection.
Key Components
- Permanent Magnet: Creates a radial magnetic field
- Soft Iron Core: Concentrates magnetic field and makes it uniform
- Rectangular Coil: Multiple turns of fine copper wire
- Springs: Provide restoring torque and current paths
- Pointer: Indicates deflection on a calibrated scale
Working Principle
- Current passes through the coil via springs
- Coil experiences forces due to interaction with magnetic field
- Forces form a couple, producing a torque that rotates the coil
- Deflection is opposed by springs’ restoring torque
- At equilibrium, magnetic torque equals spring torque
- Deflection is proportional to current through the coil
Moving Coil Galvanometer Construction
Mathematical Analysis
Torque on the Coil
τ = NBIA sin θ
B = Magnetic field strength
A = Area of the coil
Restoring Torque
τs = kϕ
Where k is spring constant and ϕ is angular deflection
At Equilibrium
NBIA = kϕ
ϕ = (NBIA/k)
Therefore, ϕ ∝ I (deflection is proportional to current)
Applications and Modifications
Ammeter
Galvanometer with low resistance shunt connected in parallel to measure current
Voltmeter
Galvanometer with high resistance connected in series to measure voltage
Ballistic Galvanometer
Special design with heavy coil to measure charge or magnetic flux
Page 9 of 18
Introduction to Magnetism and Matter
Magnetism in Materials
Magnetism in materials arises from the motion of electrons, which creates tiny current loops and hence magnetic moments.
Origins of Magnetism
- Orbital Motion: Electrons orbiting the nucleus create magnetic moments
- Spin Motion: Intrinsic spin of electrons produces magnetic moments
- Nuclear Magnetism: Much weaker effect from nuclear spins
Key Magnetic Quantities
Magnetic Field Intensity (H): The magnetizing field applied to a material
Unit: Ampere/meter (A/m)
Magnetization (M): Magnetic moment per unit volume of the material
Unit: Ampere/meter (A/m)
Magnetic Flux Density (B): B = μ₀(H + M)
Unit: Tesla (T) or Weber/m²
Magnetic Susceptibility (χₘ): M = χₘH
Dimensionless quantity that indicates how magnetizable a material is
Magnetic Domains
Ferromagnetic materials contain domains with aligned magnetic moments. External magnetic fields can align these domains.
Classification of Magnetic Materials
Diamagnetic
Weakly repelled by magnetic fields
χₘ is small and negative
Examples: Bismuth, Gold, Silver, Water
Paramagnetic
Weakly attracted to magnetic fields
χₘ is small and positive
Examples: Aluminum, Platinum, Oxygen
Ferromagnetic
Strongly attracted to magnetic fields
χₘ is large and positive
Examples: Iron, Cobalt, Nickel
Magnetic Behavior: Temperature Dependence
Curie Temperature
Ferromagnetic materials become paramagnetic above their Curie temperature
Curie’s Law
For paramagnetic materials: χₘ ∝ 1/T
Susceptibility decreases with temperature
Diamagnetism
χₘ is negative and nearly independent of temperature
Present in all materials but often overshadowed
Page 10 of 18
Bar Magnets and Their Properties
Properties of Bar Magnets
- Magnetic Poles: Each bar magnet has two poles – North (N) and South (S). Like poles repel, unlike poles attract.
- Inseparability: Magnetic poles always exist in pairs. If a magnet is broken, each piece becomes a complete magnet with both poles.
- Magnetic Axis: The line joining the North and South poles of a magnet is called its magnetic axis.
- Directive Property: When suspended freely, a bar magnet aligns itself in the north-south direction, with its North pole pointing toward geographic North.
- Magnetic Field Lines: They originate from the North pole and terminate at the South pole outside the magnet, forming closed loops.
Magnetic Moment
The magnetic moment (⃗m) of a bar magnet is a vector quantity that determines the torque it will experience in a magnetic field.
⃗m = m · ⃗l
Where m is the pole strength and l is the magnetic length
The direction of the magnetic moment is from the South pole to the North pole of the magnet.
Magnetic Field Lines of a Bar Magnet
Magnetic Field Due to a Bar Magnet
Axial Line
B = μ₀/(4π) · 2M/r³
Where M is magnetic moment
Equatorial Line
B = -μ₀/(4π) · M/r³
Field is half as strong as on axial line
Interaction Between Bar Magnets
Opposite poles attract
Like poles repel
Page 11 of 18
Earth’s Magnetism
Earth as a Magnet
Earth behaves like a giant bar magnet with its magnetic axis tilted approximately 11° from its geographic axis.
Key Facts
- Earth’s magnetic North pole is actually a south magnetic pole (it attracts the north pole of a compass needle)
- Earth’s magnetic field extends far into space, creating the magnetosphere which protects against solar wind
- The magnitude of Earth’s magnetic field at the surface ranges from 25 to 65 μT (0.25 to 0.65 Gauss)
- Earth’s magnetic field is believed to be generated by convection currents in its liquid outer core (dynamo theory)
Magnetic Elements
Declination (δ): The angle between magnetic meridian and geographic meridian at a place
Inclination or Dip (I): The angle between the total magnetic field vector and the horizontal
Horizontal Component (H): The component of Earth’s magnetic field along the horizontal
Relationship: B = √(H² + Z²) and tan I = Z/H, where Z is the vertical component
Earth’s Magnetic Field Model
Declination
Declination (δ) varies with location and time due to the shifting of Earth’s magnetic field
Inclination or Dip
Variations in Earth’s Magnetic Field
Spatial Variations
The strength and direction of Earth’s magnetic field vary with location on Earth’s surface
Secular Variations
Slow changes in Earth’s magnetic field over time, including occasional complete pole reversals
Magnetic Storms
Temporary disturbances in Earth’s magnetosphere caused by solar activity
Page 12 of 18
Magnetization and Magnetic Intensity
Magnetization (M)
Magnetization is a vector quantity that measures how strongly a material is magnetized. It represents the density of magnetic dipole moments in the material.
Definition
⃗M = Σ⃗m/V
Where Σ⃗m is sum of all magnetic moments in volume V
Key Points
- Unit: Ampere/meter (A/m)
- Direction: Indicates the orientation of the aligned magnetic moments in the material
- Effect: Produces an additional magnetic field inside the material
- In paramagnetic and diamagnetic materials, M is proportional to applied field H
- In ferromagnetic materials, M is non-linear and shows hysteresis
Magnetization Process
Magnetic Intensity (H)
Magnetic intensity (H) is a vector quantity that represents the magnetizing field used to generate magnetic induction in a material.
Definition
⃗H = ⃗B/μ₀ – ⃗M
Where B is magnetic flux density and μ₀ is permeability of free space
Properties
- • Unit: Ampere/meter (A/m)
- • Independent of the material
- • Determined by external currents
- • Related to B by material’s response
Field Inside Materials
B = μ₀(H + M)
For linear materials: M = χₘH
Where χₘ is magnetic susceptibility
Therefore: B = μ₀μᵣH
Magnetic Susceptibility (χₘ)
Definition
M = χₘH
χₘ = M/H
Dimensionless quantity that indicates how magnetizable a material is
| Material Type | χₘ Value | Magnetic Behavior |
|---|---|---|
| Diamagnetic | Small negative (-10⁻⁶ to -10⁻⁴) | Weakly repelled by magnetic fields Examples: Bismuth, Gold, Water |
| Paramagnetic | Small positive (10⁻⁵ to 10⁻³) | Weakly attracted to magnetic fields Examples: Aluminum, Oxygen |
| Ferromagnetic | Large positive (10² to 10⁴) | Strongly attracted to magnetic fields Examples: Iron, Cobalt, Nickel |
Page 13 of 18
Types of Magnetic Materials
Diamagnetic Materials
• χₘ is small and negative
• Slightly repelled by magnetic fields
• No permanent magnetic moments
• Examples: Bismuth, Gold, Silver, Water
Paramagnetic Materials
• χₘ is small and positive
• Weakly attracted to magnetic fields
• Contains unpaired electrons
• Examples: Aluminum, Oxygen, Platinum
Ferromagnetic Materials
• χₘ is large and positive (10² to 10⁴)
• Strongly attracted to magnetic fields
• Forms magnetic domains
• Examples: Iron, Cobalt, Nickel
Magnetic Domains
• Regions with uniform magnetization direction
• Separated by domain walls or boundaries
• In unmagnetized state, domains are randomly oriented, resulting in zero net magnetization
• When external field is applied, domains aligned with field grow at expense of others
• Domain wall motion is responsible for magnetization process
Hysteresis Loop
• Shows relationship between B and H for ferromagnetic materials
• Remanence: Magnetization that remains when external field is removed
• Coercivity: Reverse field needed to demagnetize the material
• Saturation: Maximum possible magnetization
• Area inside loop represents energy loss per cycle (hysteresis loss)
• Hard magnets: Wide loop, high remanence (permanent magnets)
• Soft magnets: Narrow loop, low remanence (transformers)
Special Types of Magnetic Materials
Antiferromagnetic
Adjacent atomic magnetic moments align in opposite directions, resulting in zero net magnetization
Examples: Manganese Oxide, Chromium
Ferrimagnetic
Adjacent moments align antiparallel but with unequal magnitudes, resulting in net magnetization
Examples: Ferrites, Magnetite (Fe₃O₄)
Superparamagnetic
Nano-sized ferromagnetic particles that behave like paramagnets due to thermal fluctuations
Used in magnetic recording media and biomedical applications
Page 14 of 18
Applications of Magnetic Effects and Magnetism
Electric Motors
Principle: Force on current-carrying conductors in magnetic fields
Used in fans, electric vehicles, appliances, and industrial machinery to convert electrical energy to mechanical energy
Generators
Principle: Electromagnetic induction – changing magnetic flux induces EMF
Used in power plants, wind turbines, and hydroelectric dams to convert mechanical energy into electrical energy
Transformers
Principle: Mutual induction between coils sharing magnetic flux
Used in power distribution systems to step-up/step-down voltage for efficient power transmission
Speakers & Microphones
Use interaction between current-carrying coil and magnetic field to convert electrical signals to sound (speakers) or sound to electrical signals (microphones)
MRI Scanners
Uses strong magnetic fields (0.5-3 Tesla) and radio waves to generate detailed images of internal body structures by detecting hydrogen nuclei alignment in tissues
Data Storage
Hard drives, magnetic tapes, and credit cards store data by magnetizing tiny regions on ferromagnetic materials in specific patterns to represent binary information
Emerging Applications
Maglev Trains
Use magnetic levitation and propulsion to achieve high speeds (up to 600 km/h) with minimal friction
Particle Accelerators
Use powerful electromagnets to guide and accelerate charged particles to near light speed for scientific research
Magnetic Nanoparticles
Used in targeted drug delivery, cancer treatment, and medical imaging to improve therapeutic efficacy
Page 15 of 18
Important Formulas and Relationships
Magnetic Field Due to Current
Biot-Savart Law:
dB = μ0 / 4π · Idl × r̂ / r2
Straight Wire:
B = μ0I / 2πr
Circular Loop (center):
B = μ0I / 2R
Solenoid:
B = μ0nI
n = number of turns per unit length
Toroid:
B = μ0NI / 2πr
N = total number of turns
Ampere’s Circuital Law:
∮ B · dl = μ0Ienc
Forces and Torques
Force on Moving Charge:
F = q(v × B)
|F| = |q|vB sin θ
Force on Current-Carrying Conductor:
F = I(L × B)
|F| = ILB sin θ
Torque on Current Loop:
τ = m × B
|τ| = mB sin θ
m = IA (magnetic moment)
Magnetism in Materials
Magnetic Field Relations:
B = μ0(H + M)
M = χmH
B = μ0μrH
μr = 1 + χm (relative permeability)
Diamagnetic Materials:
χm < 0 (small negative)
μr < 1
Paramagnetic Materials:
χm > 0 (small positive)
μr > 1
Ferromagnetic Materials:
χm >> 0 (large positive)
μr >> 1
Curie’s Law:
χm ∝ 1/T
(for paramagnetic materials)
Earth’s Magnetism
Magnetic Elements:
Declination (δ)
Angle between magnetic and geographic meridian
Inclination/Dip (I)
Angle between B and horizontal
Horizontal Component (H)
B cos I
Relationship Between Components:
B = √(H² + Z²)
Z is vertical component
tan I = Z/H
I = 90° at magnetic poles
I = 0° at magnetic equator
Applications of Formulas in Problem Solving
Motion of charged particles in magnetic fields
Current-carrying conductors in magnetic fields
Analysis of Earth’s magnetic field components
Behavior of different magnetic materials
Page 16 of 18
Solved Examples: Magnetic Effects and Magnetism
Force on a Moving Charge
An electron moving with a velocity of 2.0 × 10⁶ m/s enters a magnetic field of 0.3 T perpendicular to its direction. Calculate the force experienced by the electron.
Given:
Charge (q) = -1.6 × 10⁻¹⁹ C
Velocity (v) = 2.0 × 10⁶ m/s
Magnetic field (B) = 0.3 T
Angle (θ) = 90°
Formula:
F = q(v × B) = qvB sin θ
Solution:
F = (-1.6 × 10⁻¹⁹)(2.0 × 10⁶)(0.3)(sin 90°)
F = (-1.6 × 10⁻¹⁹)(2.0 × 10⁶)(0.3)(1)
F = -9.6 × 10⁻¹⁴ N
The force is 9.6 × 10⁻¹⁴ N, perpendicular to both v and B.
Magnetic Field Due to a Conductor
Calculate the magnetic field at a point 5 cm away from a long straight wire carrying a current of 10 A.
Given:
Current (I) = 10 A
Distance (r) = 5 cm = 0.05 m
μ₀ = 4π × 10⁻⁷ T·m/A
Formula:
B = μ₀I / 2πr
Solution:
B = (4π × 10⁻⁷ × 10) / (2π × 0.05)
B = (4 × 10⁻⁷ × 10) / (0.1)
B = 4 × 10⁻⁶ T
The magnetic field is 4 × 10⁻⁵ gauss or 4 × 10⁻⁶ tesla.
Earth’s Magnetic Field Components
At a certain location, the horizontal component of Earth’s magnetic field is 0.3 × 10⁻⁴ T and the angle of dip is 60°. Calculate the total magnetic field and its vertical component.
Given:
Horizontal component (H) = 0.3 × 10⁻⁴ T
Angle of dip (I) = 60°
Formulas:
tan I = Z/H
B = √(H² + Z²)
Solution:
Z = H × tan I
Z = 0.3 × 10⁻⁴ × tan 60°
Z = 0.3 × 10⁻⁴ × 1.732
Z = 0.52 × 10⁻⁴ T
B = √(H² + Z²)
B = √((0.3 × 10⁻⁴)² + (0.52 × 10⁻⁴)²)
B = √(0.09 × 10⁻⁸ + 0.27 × 10⁻⁸)
B = √(0.36 × 10⁻⁸)
B = 0.6 × 10⁻⁴ T
Problem-Solving Tips
Identify relevant variables
List all given values and convert to SI units if necessary
Select appropriate formula
Choose the correct equation based on the physical situation described
Pay attention to vectors
Remember that magnetic fields, forces, and velocities are vector quantities
Page 17 of 18
Summary and Conclusion
Key Concepts We’ve Covered
Magnetic Field
The region around a magnet or current-carrying conductor where magnetic influence can be detected
Biot-Savart Law
Relates magnetic field to the magnitude, direction, and proximity of the electric current that creates it
Ampere’s Law
Relates the integrated magnetic field around a closed loop to the electric current passing through it
Lorentz Force
Force on a charged particle moving through electric and magnetic fields
Magnetic Torque
Torque experienced by a current loop or magnetic dipole in a magnetic field
Earth’s Magnetism
The magnetic field of Earth, its origins, properties and elements (declination, inclination, etc.)
Classification of Magnetic Materials
Diamagnetic
Weakly repelled by magnetic fields (Bismuth, Gold)
Paramagnetic
Weakly attracted to magnetic fields (Aluminum, Oxygen)
Ferromagnetic
Strongly attracted to magnetic fields (Iron, Cobalt, Nickel)
Special Types
Antiferromagnetic, Ferrimagnetic, Superparamagnetic
Practical Applications
Electric Motors
Convert electrical energy to mechanical energy
Generators
Convert mechanical energy to electrical energy
Transformers
Transfer electrical energy between circuits
Speakers
Convert electrical signals to sound waves
MRI Scanners
Medical imaging using magnetic fields
Data Storage
Hard drives and magnetic storage media
Important Formulas to Remember
Biot-Savart Law
dB = (μ₀/4π) · (Idl × r̂)/r²
Ampere’s Law
∮ B·dl = μ₀Ienc
Lorentz Force
F = q(v × B)
Magnetic Torque
τ = m × B
Further Study and Exploration
NCERT Physics Textbooks
Chapters 4 and 5 for in-depth understanding
Laboratory Experiments
Hands-on activities to verify magnetic concepts
Online Simulations
Interactive visualization of magnetic phenomena
Remember: The fascinating interplay between electricity and magnetism is foundational to many technologies that power our modern world!
Page 18 of 18
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