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Physics Department • Class 10 ICSE Master Series
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CHAPTER 10: ELECTROMAGNETISM
ELECTROMAGNETISM
Official ICSE Syllabus & Scope
Core Syllabus Topics Covered:
- Magnetic Effect of Electric Current: Oersted's experiment; magnetic field ($B$) and field lines due to current in a straight wire; Right-Hand Thumb Rule; magnetic field due to current in a circular loop (Clock Face Rule); Solenoids; Electromagnets (construction, factors increasing strength, uses, comparison with permanent magnets, Electric Bell).
- Force on Current-Carrying Conductor & DC Motor: Fleming's Left-Hand Rule; DC electric motor — simple sketch of main parts (armature coil, field magnet, split-ring commutator, carbon brushes), brief description and type of energy transfer (working not required).
- Electromagnetic Induction (EMI) & AC Generator: Simple introduction to EMI; Faraday's experiments; Lenz's law; Fleming's Right-Hand Rule; AC Generator — simple sketch of main parts (coil, magnet, slip rings, brushes), brief description and energy transfer; frequency of household AC ($50\text{ Hz}$); advantages of AC over DC.
- Transformers: Principle (Mutual Induction); types (Step-Up and Step-Down); characteristics of primary and secondary coils (turns ratio, thickness of wires); simple labeled diagrams, equations ($\frac{V_s}{V_p} = \frac{N_s}{N_p} = \frac{I_p}{I_s}$), energy losses, and practical uses.
1. Magnetic Effect of Electric Current & Field Patterns
Oersted's Historic Experiment (1820)
Hans Christian Oersted discovered that an electric current flowing through a conductor creates a magnetic field in its surrounding space.
Figure 10.1 & 10.2: Oersted's Experiment Setup & Reversal of Deflection
Observations & SNOW Rule
- When no current flows, a magnetic compass needle aligns with the Earth's geographic North-South direction.
- When current flows from South to North in a wire held OVER the needle: The North pole of the needle deflects towards the West.
- When current direction is reversed (North to South): The North pole deflects towards the East.
- When wire is placed BELOW the needle: The deflection direction is reversed.
- Deflection Magnitude: Increases upon increasing the current ($I$) and upon bringing the needle closer to the wire.
The SNOW Rule: South → North, held Over &implies; Deflection towards West
Properties of Magnetic Field Lines
Fundamental Properties of Magnetic Field Lines
- Continuous Closed Loops: Magnetic field lines emerge from the North pole and enter the South pole outside the magnet, and continue from the South pole to the North pole inside the magnet.
- Direction of Field: The tangent drawn at any point on a magnetic field line gives the direction of the magnetic field vector ($\vec{B}$) at that point.
- Never Intersect: Two magnetic field lines can never intersect each other. If they did, at the point of intersection there would be two tangents, meaning two different directions of magnetic field at the same point, which is physically impossible.
- Relative Density Indicates Strength: The field lines are crowded in regions where the magnetic field is strong (near the poles) and spread apart where the field is weak.
- Neutral Points: Points where the magnetic field produced by the current/magnet is equal in magnitude and opposite in direction to the horizontal component of Earth's magnetic field ($B_H$). At a neutral point, the resultant magnetic field is zero, and a compass needle can point in any arbitrary direction.
Magnetic Field Due to a Straight Current-Carrying Conductor
When current passes vertically through a straight wire passing through a horizontal cardboard sprinkled with iron filings:
Figure 10.3 & 10.4: Magnetic Field of Straight Conductor & Right-Hand Thumb Rule
Field Strength Relationships
- Concentric Circles: The magnetic field lines form concentric circles centered on the wire in planes perpendicular to the wire.
- Dependence on Current ($I$): $B \propto I$ — Directly proportional to the current magnitude.
- Dependence on Distance ($r$): $B \propto \frac{1}{r}$ — Inversely proportional to the distance from the wire.
Rules for Direction of Magnetic Field
| Rule Name |
Statement / Description |
Application |
| Right-Hand Thumb Rule |
Hold the wire in your right hand with the thumb pointing in current direction. The curled fingers give the direction of magnetic field lines. |
Straight wires & coils. |
| Maxwell's Corkscrew Rule |
If a right-handed corkscrew is turned so that it advances in the direction of current, the direction of rotation gives the magnetic field direction. |
Alternative for straight conductors. |
| Clock Face Rule |
Looking directly at a circular loop face:
• Clockwise current → South Pole (S)
• Anticlockwise current → North Pole (N) |
Polarity of circular coils & solenoids. |
Magnetic Field Due to a Circular Loop / Coil
Figure 10.5 & 10.6: Magnetic Field in Circular Coil & Clock Face Rule
Circular Coil Field Behavior
- Near the wire segments, field lines are concentric circles.
- As we move towards the center of the loop, the circles become larger and larger arcs.
- At the center of the circular loop, the magnetic field lines are practically straight, parallel, and perpendicular to the plane of the loop, forming a uniform field.
- Factors Affecting Field at Center of Coil:
$$ B = \frac{\mu_0 \cdot N \cdot I}{2 \cdot r} $$
- $B \propto I$ — Directly proportional to current.
- $B \propto N$ — Directly proportional to the number of turns in the coil.
- $B \propto \frac{1}{r}$ — Inversely proportional to the radius of the coil.
Magnetic Field in a Solenoid
Figure 10.7 & 10.8: Magnetic Field of Solenoid & Comparison with Bar Magnet
Comparison: Solenoid vs Permanent Bar Magnet
| Feature |
Current-Carrying Solenoid |
Permanent Bar Magnet |
| Magnetic Field Pattern |
Produces identical dipolar magnetic field lines. |
Produces identical dipolar magnetic field lines. |
| Control of Magnetism |
Magnetism can be switched ON or OFF instantly. |
Magnetism is permanent and cannot be switched off. |
| Magnetic Strength |
Can be made extremely strong by increasing current or turns. |
Fixed and comparatively weak. |
| Reversibility of Poles |
Poles can be easily reversed by reversing current direction. |
Poles are permanently fixed. |
✍ CLASSROOM EXEMPLAR A1: RIGHT-HAND THUMB RULE ON HORIZONTAL WIRE
Problem: A horizontal power line carries current from East to West. Find the magnetic field direction at a point (i) directly below it, (ii) directly above it.
Solution:
Applying the Right-Hand Thumb Rule with the thumb pointing West:
- (i) Directly below the wire: The curled fingers point towards North.
- (ii) Directly above the wire: The curled fingers curl around and point towards South.
2. Electromagnets & Practical Applications (The Electric Bell)
Structure & Types of Electromagnets
An electromagnet is a temporary magnet formed by winding insulated copper wire around a soft iron core.
Figure 10.9 & 10.10: I-Shaped Bar & U-Shaped (Horseshoe) Electromagnets
| Type |
Design & Construction |
Common Uses |
| I-Shaped (Bar) Electromagnet |
Straight cylindrical soft iron bar with copper wire wound over it. Poles are at opposite ends. |
Relays, small buzzers. |
| U-Shaped (Horseshoe) Electromagnet |
Wound over a U-shaped soft iron core with opposite windings on the two arms. Brings North and South poles close together for high magnetic flux concentration. |
Electric bells, heavy scrap lifting cranes, Maglev trains, DC motors. |
Comprehensive Comparison: Electromagnet vs Permanent Magnet
| Property |
Electromagnet (Soft Iron Core) |
Permanent Magnet (Steel / Alnico) |
| Nature of Magnetism |
Temporary — easily demagnetized by switching off current. |
Permanent — retains magnetism for long durations. |
| Magnetic Strength |
Very Strong & Easily Variable (by adjusting current $I$ or turns $n$). |
Fixed & Comparatively Weak. |
| Polarity |
Reversible by reversing the direction of current. |
Fixed and cannot be reversed easily. |
| Core Material & Magnetic Properties |
Soft Iron (High magnetic permeability, low retentivity & low coercivity). |
Carbon Steel / Alnico / Nipermag (High retentivity & high coercivity). |
Soft iron has high magnetic permeability (gets strongly magnetized quickly) and very low retentivity/coercivity (loses almost all magnetism instantly when current is turned off). If steel were used, it would retain permanent magnetism and fail to release the armature in devices like electric bells or scrap cranes!
The Electric Bell (Key ICSE Board Application)
The Electric Bell is a direct practical application of a U-shaped electromagnet operating on the principle of continuous make-and-break of an electric circuit.
Figure 10.11: Complete Circuit & Working Assembly of an Electric Bell
Main Components & Working Cycle of Electric Bell
- Main Components:
- U-shaped Electromagnet ($M$): Soft iron core wound with insulated copper wire.
- Soft Iron Armature ($A$): Mounted on a flexible flat spring ($S$).
- Hammer ($H$) and Gong ($G$): Attached to the armature to strike the bell gong.
- Contact Adjusting Screw ($T$): Makes electrical contact with the flat spring.
- Step-by-Step Working Mechanism:
- When the push switch ($K$) is pressed, current flows through the electromagnet coil, magnetizing the soft iron core.
- The electromagnet attracts the soft iron armature. As the armature moves forward, the hammer strikes the metallic gong, producing a sound.
- As the armature moves forward, the flat spring pulls away from the tip of the contact screw ($T$), breaking the electric circuit.
- The moment current stops, the electromagnet loses its magnetism. The spring pulls the armature back to its original position, restoring contact with screw $T$.
- The circuit is completed again, current flows, and the cycle repeats automatically as long as the switch is held pressed, producing a continuous ringing sound.
✍ CLASSROOM EXEMPLAR B1: WAYS TO INCREASE ELECTROMAGNET STRENGTH
Problem: State three practical methods by which the magnetic strength of an electromagnet can be increased.
Solution:
- By increasing the electric current ($I$) flowing through the coil windings.
- By increasing the total number of turns ($n$) of the insulated copper wire.
- By using a U-shaped soft iron core so that both poles are brought close together.
3. Force on a Conductor & DC Electric Motor
Force on a Current-Carrying Conductor in a Magnetic Field
Figure 10.12 & 10.13: Force on Conductor (Kicking Wire) & Fleming's Left-Hand Rule
Lorentz Force Principle & Kicking Wire Demonstration
When a current-carrying conductor is placed inside an external magnetic field, it experiences a mechanical force:
$$ F = I \cdot L \cdot B \cdot \sin\theta $$
- Maximum Force ($F_{\text{max}} = ILB$): When the conductor is perpendicular to the field ($\theta = 90^\circ$).
- Zero Force ($F = 0$): When the conductor is parallel to the field ($\theta = 0^\circ$ or $180^\circ$).
- Kicking Wire Experiment: A flexible copper wire suspended between the poles of a strong horseshoe magnet dips into mercury. When current is switched on, the wire kicks forward and jumps out of the mercury bath (breaking the circuit), falls back under gravity, and kicks again continuously.
Fleming's Left-Hand Rule (Motor Rule)
Fleming's Left-Hand Rule (FBI)
Stretch the thumb, forefinger, and middle finger of your LEFT hand mutually perpendicular to each other:
- Forefinger ($\mathbf{F}$ield): Points in the direction of the Magnetic Field ($B$).
- Center / Middle Finger ($\mathbf{C}$urrent): Points in the direction of Electric Current ($I$).
- Thumb ($\mathbf{M}$otion / $\mathbf{F}$orce): Points in the direction of Mechanical Force / Motion ($F$).
The Direct Current (DC) Electric Motor
A DC Motor is an electrical machine that converts Electrical Energy into Mechanical (Rotational) Energy.
Figure 10.14 & 10.15: DC Electric Motor Assembly & Split-Ring Commutator Action
| Component |
Specific Function in DC Motor |
| Armature Coil ($ABCD$) |
Many turns of insulated copper wire wound over a soft iron core. Carries current and experiences a rotational deflecting couple (torque). |
| Field Magnet |
Provides a strong magnetic field. Concave poles create a radial magnetic field so that the plane of the coil remains parallel to field lines for maximum torque. |
| Split-Ring Commutator ($S_1, S_2$) |
A copper ring split into two insulated halves. Reverses the current direction through the coil every half-rotation ($180^\circ$) to maintain unidirectional rotation. |
| Carbon Brushes ($B_1, B_2$) |
Flexible graphite blocks that maintain continuous sliding electrical contact between the rotating split rings and the stationary DC source. |
Factors Increasing Speed & Rotational Power of DC Motor
- By increasing the electric current ($I$) through the armature coil.
- By increasing the total number of turns ($N$) of the armature coil.
- By increasing the area ($A$) of the armature coil.
- By using a stronger field magnet ($B$).
- By winding the armature coil on a laminated soft iron core.
✍ CLASSROOM EXEMPLAR C1: ROLE OF SPLIT-RING COMMUTATOR
Problem: State the function of the split-ring commutator in a DC electric motor. What would happen if slip rings were used instead?
Solution:
- Function: It automatically reverses the current direction in arms $AB$ and $CD$ after every half rotation, ensuring that the couple acting on the coil continues to rotate it in the same direction.
- If Slip Rings Were Used: The current direction would not reverse, and the coil would merely oscillate back and forth between $0^\circ$ and $180^\circ$ instead of rotating continuously.
4. Electromagnetic Induction (EMI) & AC Generator
Faraday's Experiments on Electromagnetic Induction
Electromagnetic Induction is the phenomenon of producing an induced EMF (and induced current) in a closed circuit whenever the magnetic flux linked with the circuit changes with time.
Figure 10.16 & 10.17: Faraday's Electromagnetic Induction Experiments
| Experiment Setup |
Observation |
Key Inference |
| 1. Moving Magnet into Coil |
North pole plunged into coil → Galvanometer deflects momentarily right. Magnet held stationary inside → Deflection drops to zero. North pole withdrawn → Deflects in opposite direction (left). |
Relative motion between coil and magnet produces induced current. Faster motion produces larger deflection. |
| 2. Moving Coil near Magnet |
Holding magnet stationary and moving the coil produces identical deflections in the galvanometer. |
It is the relative change of magnetic flux linked with the circuit that induces EMF. |
| 3. Two Coils (Primary & Secondary) |
When key is pressed in Primary coil → Secondary galvanometer gives momentary kick. When steady current flows → Deflection is zero. When key is released → Momentary deflection in opposite direction. |
Changing primary current changes magnetic flux in secondary coil (Mutual Induction). |
Faraday's Laws & Mathematical Formula
- First Law: An EMF is induced in a coil whenever there is a change in the magnetic flux linked with it. The induced EMF persists as long as the flux change continues.
- Second Law: The magnitude of the induced EMF is directly proportional to the rate of change of magnetic flux linked with the coil:
$$ e = -N \frac{\Delta \Phi}{\Delta t} $$
Direction of Induced Current: Lenz's Law & Fleming's Right-Hand Rule
| Principle / Rule |
Statement / Principle |
Physics Significance |
| Lenz's Law |
The direction of induced EMF/current is always such that it opposes the very cause (change in magnetic flux) that produces it. |
Direct manifestation of the Law of Conservation of Energy. Mechanical work done against repulsion/attraction is converted to electrical energy. |
| Fleming's Right-Hand Rule (Generator Rule) |
Stretch thumb, forefinger, and middle finger of the RIGHT hand mutually perpendicular:
• Thumb: Direction of Motion of conductor.
• Forefinger: Direction of Magnetic Field.
• Middle Finger: Direction of Induced Current. |
Determines direction of induced current in dynamic generators. |
The Alternating Current (AC) Generator (Alternator)
An AC Generator converts Mechanical Energy into Electrical Energy (Alternating Current) via electromagnetic induction.
Figure 10.18 & 10.19: AC Generator (Alternator) Assembly & Output Sinusoidal Waveform
Household AC in India & Advantages of AC over DC
Indian Household AC Supply Metrics
- Voltage: $220\text{ V}$ (RMS value).
- Frequency: $f = 50\text{ Hz}$ ($50\text{ cycles/second}$).
- Direction Reversals: In each cycle, current reverses direction twice — thus changing direction $100\text{ times per second}$!
- Time Period: $T = \frac{1}{f} = \frac{1}{50}\text{ s} = \mathbf{0.02\text{ seconds}}$.
| Parameter |
Alternating Current (AC) |
Direct Current (DC) |
| Direction & Magnitude |
Magnitude changes continuously; direction reverses periodically. |
Constant magnitude; unidirectional flow. |
| Voltage Transformation |
Voltage can be stepped up or down efficiently using transformers. |
Cannot be stepped up or down easily using simple transformers. |
| Long-Distance Transmission |
Transmitted over hundreds of kilometers at high voltage ($132\text{ kV}$) with minimal $I^2R$ power loss. |
Substantial line power losses over long distances. |
✍ CLASSROOM EXEMPLAR D1: AC PERIOD & REVERSALS CALCULATION
Problem: In India, the frequency of domestic AC supply is $50\text{ Hz}$. Calculate (i) the time period of one cycle, (ii) the number of times current changes direction in $1\text{ second}$.
Solution:
- (i) Time Period: $T = \frac{1}{f} = \frac{1}{50}\text{ s} = \mathbf{0.02\text{ s}}$.
- (ii) Direction Changes: In 1 cycle, current changes direction $2$ times. In 50 cycles (1 second), direction changes $= 50 \times 2 = \mathbf{100\text{ times}}$.
5. Transformers (Step-Up & Step-Down)
Principle & Core Construction
A Transformer is a static electrical machine used to transform alternating voltage from one level to another on the principle of Mutual Induction.
Figure 10.20 & 10.21: Step-Up and Step-Down Transformers on Laminated Soft Iron Cores
Transformer Architecture
- Laminated Soft Iron Core: Built up of thin silicon steel sheets insulated with varnish to minimize eddy current heat losses.
- Primary Coil ($P$): Connected to input AC source ($V_p, I_p, N_p$).
- Secondary Coil ($S$): Connected to output electrical load ($V_s, I_s, N_s$).
Comparison: Step-Up vs Step-Down Transformers
| Characteristic |
Step-Up Transformer |
Step-Down Transformer |
| Voltage Action |
Increases AC Voltage ($\mathbf{V_s > V_p}$). |
Decreases AC Voltage ($\mathbf{V_s < V_p}$). |
| Current Action |
Decreases AC Current ($\mathbf{I_s < I_p}$). |
Increases AC Current ($\mathbf{I_s > I_p}$). |
| Turns Ratio ($n = \frac{N_s}{N_p}$) |
$\mathbf{N_s > N_p} \implies n > 1$. |
$\mathbf{N_s < N_p} \implies n < 1$. |
| Wire Thickness |
Primary coil has thicker wire (handles high $I_p$); Secondary has thinner wire with more turns. |
Primary coil has thinner wire; Secondary coil has thicker wire with fewer turns (handles heavy $I_s$ without overheating). |
| Applications |
Power generating stations ($11\text{ kV} \to 132\text{ kV}$), X-ray machines. |
City distribution sub-stations ($132\text{ kV} \to 220\text{ V}$), mobile chargers ($220\text{ V} \to 5\text{ V}$), doorbells. |
Transformer Mathematical Equations
TRANSFORMATION FORMULAS
$$ \frac{V_s}{V_p} = \frac{N_s}{N_p} = \frac{I_p}{I_s} = n $$
$$ \text{Input Power } P_{\text{in}} = V_p I_p \quad \text{and} \quad \text{Output Power } P_{\text{out}} = V_s I_s $$
$$ \text{Efficiency } \eta = \frac{V_s I_s}{V_p I_p} \times 100\% $$
For an ideal ($100\%$ efficient) transformer: $V_s I_s = V_p I_p$.
Energy Losses in a Practical Transformer
| Loss Type |
Cause |
Remedy / Prevention |
| 1. Copper Loss |
$I^2R$ Joule heating in the primary and secondary copper windings. |
Use thick copper wires of low electrical resistance. |
| 2. Eddy Current Loss |
Induced circulating currents in the iron core producing heat. |
Use a laminated core insulated with varnish. |
| 3. Hysteresis Loss |
Repeated magnetization and demagnetization cycles of the core. |
Use soft iron / silicon steel with low hysteresis loss. |
| 4. Flux Leakage |
Incomplete linking of magnetic flux between primary and secondary. |
Winding secondary directly over primary (Shell-type core). |
| 5. Humming Loss |
Magnetostriction causing mechanical vibrations in core plates. |
Tightly clamped core laminations. |
✍ CLASSROOM EXEMPLAR E1: STEP-DOWN TRANSFORMER TURNS & CURRENT
Problem: A step-down transformer has $5000\text{ turns}$ in its primary coil connected to a $220\text{ V}$ AC mains. The output secondary voltage is $11\text{ V}$. Find:
(i) The number of turns in the secondary coil.
(ii) The primary current when secondary supplies $20\text{ A}$ (assume $100\%$ efficiency).
Solution:
- (i) Secondary Turns ($N_s$):
$$ \frac{N_s}{N_p} = \frac{V_s}{V_p} \implies \frac{N_s}{5000} = \frac{11}{220} = \frac{1}{20} \implies N_s = \frac{5000}{20} = \mathbf{250\text{ turns}} $$
- (ii) Primary Current ($I_p$):
$$ V_p I_p = V_s I_s \implies 220 \times I_p = 11 \times 20 \implies I_p = \frac{220}{220} = \mathbf{1.0\text{ A}} $$
✍ CLASSROOM EXEMPLAR E2: STEP-UP TRANSFORMER EFFICIENCY
Problem: A step-up transformer operates on $220\text{ V}$ and delivers $2200\text{ V}$ to a load drawing $2\text{ A}$. If the efficiency of the transformer is $80\%$, calculate the current drawn by the primary coil.
Solution:
- Output Power: $P_{\text{out}} = V_s I_s = 2200\text{ V} \times 2\text{ A} = 4400\text{ W}$.
- Input Power: Since $\eta = \frac{P_{\text{out}}}{P_{\text{in}}} \implies 0.80 = \frac{4400}{P_{\text{in}}} \implies P_{\text{in}} = \frac{4400}{0.80} = 5500\text{ W}$.
- Primary Current ($I_p$):
$$ P_{\text{in}} = V_p I_p \implies 5500 = 220 \times I_p \implies I_p = \frac{5500}{220} = \mathbf{25\text{ A}} $$
6. ICSE Board Examination Masterclass
⭐ CRITICAL ICSE CONCEPTUAL QUESTIONS
1. Why cannot a transformer work on Direct Current (DC)?
A transformer operates strictly on Mutual Induction, which requires a continuous change in magnetic flux ($\frac{\Delta \Phi}{\Delta t} \ne 0$). A DC source produces constant current ($\frac{\Delta \Phi}{\Delta t} = 0$), so no EMF is induced in the secondary. Furthermore, low primary coil resistance will draw enormous DC current, resulting in overheating and burnout.
2. Fleming's Left-Hand vs Right-Hand Rules
Left-Hand Rule: Used in Electric Motors to determine the direction of mechanical force on a current-carrying conductor in a magnetic field.
Right-Hand Rule: Used in Electric Generators to determine the direction of induced current generated by electromagnetic induction.
3. What happens if a coil is rotated at higher speed in an AC generator?
Increasing the speed of rotation increases the rate of change of magnetic flux ($\frac{\Delta \Phi}{\Delta t}$), thereby increasing the peak induced EMF (amplitude) and also increasing the frequency ($f$) of the generated alternating current.
7. Quick Revision Summary Matrix
| Device / Principle |
Energy Conversion / Key Formula |
Direction Rule |
Key Structural Feature |
| DC Electric Motor |
Electrical → Mechanical Energy |
Fleming's Left-Hand Rule |
Split-ring commutator reverses current every $180^\circ$. |
| AC Generator |
Mechanical → Electrical Energy |
Fleming's Right-Hand Rule |
Continuous slip rings produce sinusoidal AC ($50\text{ Hz}$). |
| Electric Bell |
Electrical → Sound Energy |
Electromagnetism & Make-Break |
U-shaped electromagnet & soft iron armature on flat spring. |
| Step-Up Transformer |
$V_s > V_p, \ N_s > N_p, \ I_s < I_p$ |
Mutual Induction |
Thick primary wire, thin secondary wire. |
| Step-Down Transformer |
$V_s < V_p, \ N_s < N_p, \ I_s > I_p$ |
Mutual Induction |
Thin primary wire, thick secondary wire. |
| Lenz's Law |
$e = -N \frac{\Delta \Phi}{\Delta t}$ |
Opposition principle |
Direct consequence of Conservation of Energy. |
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