Magnetic Effects of Electric Current – Comprehensive Notes

Historical Background & Introductory Ideas

• Hans Christian Oersted (1777–1851)

  • Accidentally discovered in $1820$ that a compass needle deflects when an electric current flows through a nearby metallic wire.

  • Demonstrated that electricity and magnetism are interrelated phenomena → foundation for electromagnetism.

  • The cgs unit of magnetic field strength, oersted, is named in his honour.

  • His work paved the way for radio, television, fibre-optics, etc.

• Link between electricity & magnetism

  • Activity 12.1: Straight thick copper wire (XY) held perpendicular to page, small compass placed near wire.

  • On closing key, compass needle deflects → current produces magnetic effect.

  • Raises reciprocal question: can moving magnets produce electric effects? (Studied in later sections)

Magnetic Field & Field Lines

• Compass needle = miniature bar magnet; north-seeking end ≡ north pole, south-seeking end ≡ south pole.

• Like poles repel, unlike poles attract.

• Magnetic field: Region around a magnet where magnetic force can be detected.

Visualising field lines

• Activity 12.2: Bar magnet under paper sprinkled with iron filings.

  • Gentle tapping reveals a characteristic pattern aligned along field lines.

• Activity 12.3: Tracing field lines with a compass

  1. Place compass near north pole, mark positions of needle ends.

  2. Move compass so its south pole occupies previous north-pole mark; repeat until south pole of magnet reached.

  3. Join successive points with a smooth curve → one field line.

  4. Repeating gives full pattern (Fig 12.4).

Properties of magnetic field lines

• Direction defined by motion of a hypothetical free north pole.

• Convention: Lines emerge from north pole and merge at south pole outside the magnet; inside magnet they run south → north, forming closed curves.

• Field strength ∝ density (closeness) of lines; strongest near poles.

• Field lines never intersect; intersection would imply contradictory directions for compass needle.

• Field at centre of long circular coil is represented by nearly parallel straight lines → indicates uniformity.

Magnetic Field due to Current-Carrying Conductors

1. Straight Conductor

• Activity 12.4 & 12.5 demonstrate:

  • Concentric circular field lines centred on wire; plane perpendicular to conductor.

  • Reversing current reverses compass deflection → field direction reverses.

  • Increasing current $I$ increases needle deflection ⇒ $B \propto I$.

  • Moving compass farther away (distance $r$) decreases deflection ⇒ $B \propto \frac1r$.

Right-Hand Thumb Rule (Maxwell’s corkscrew rule)

• Hold the conductor in right hand with thumb along current direction; curled fingers indicate magnetic-field direction.

• Example 12.1: Power line carries current east → west.

  • Point directly below wire: field points south when seen from east end (clockwise rotation).

  • Point directly above: field points north (same circle, opposite side).

2. Circular Loop

• Bending straight wire into loop: every current element produces concentric circles; at loop centre, arcs appear straight and add up.

• Field direction inside loop found by right-hand rule; field lines crowd near centre ⇒ stronger field.

• For $n$-turn coil: $B_{centre} \propto nI$ (linear superposition).

• Activity 12.6: Coil through cardboard; iron filings reveal dense straight lines through centre, closed curves outside.

3. Solenoid & Electromagnet

• Solenoid: many turns of insulated wire wound tightly on cylindrical form.

  • Field pattern (Fig 12.10) resembles bar magnet.

  • Interior field lines ≈ parallel, equally spaced ⇒ uniform $B$.

  • One end behaves as north, other as south pole (identify by right-hand screw rule).

• Electromagnet: inserting soft-iron core greatly strengthens field; magnetism persists only while current flows.

  • Used in cranes, relays, MRI, etc.

Force on a Current-Carrying Conductor in a Magnetic Field

• Ampère’s principle: Magnet exerts equal and opposite force on current-carrying conductor.

Demonstration (Activity 12.7)

• Aluminium rod AB suspended between poles of horse-shoe magnet (field vertically upward). Current B → A.

  • Rod deflects left; reversing current reverses force.

  • Interchanging magnet poles (field downwards) again reverses force.

• Factors affecting magnitude (Q 2 under Section 12.3):

  1. Higher current ⇒ larger force.

  2. Stronger magnet ⇒ larger force.

  3. Longer conductor inside field ⇒ larger force (proportional to length $l$).

Fleming’s Left-Hand Rule

• Stretch thumb, forefinger, middle finger of left hand mutually perpendicular.

  • Forefinger: magnetic field $\vec B$ (N→S).

  • Middle finger: current $\vec I$ (positive to negative direction).

  • Thumb: force/motion $\vec F$ on conductor.

• Maximum force when $\vec I$ ⟂ $\vec B$.

Example 12.2

• Electron (charge $-e$) enters field at right angles; using left-hand rule (current opposite electron motion) → force into page (option d).

Conceptual Q&A (Section 12.3)

• Physical quantities changing for proton in magnetic field: velocity & momentum (direction changes), speed & mass remain same if field uniform.

Domestic Electric Circuits

• Supply: $220\,\text{V}$, $50\,\text{Hz}$ AC provided via two-core service.

  • Live (phase): red insulation, high potential.

  • Neutral: black insulation, near earth potential.

  • Earth wire (green) connected to metal plate deep in ground.

Circuit structure (Fig 12.15)

• Incoming lines pass through main fuse & meter to distribution board.

• Separate sub-circuits:

  1. $15\,\text{A}$ rating → high-power appliances (geysers, heaters, ACs).

  2. $5\,\text{A}$ rating → lights, fans, TV, etc.

• Appliances connected in parallel so each gets full $220\,\text{V}$ and independent switching.

Safety devices & hazards

• Fuse (Section 11.7): short length of low-melt wire connected in series; melts when current exceeds rating due to Joule heating $H = I^2Rt$.

• Overloading causes:

  • Too many devices on one socket.

  • Insulation failure → live touches neutral → short-circuit (sudden large $I$).

  • Voltage surge from supply.

• Earth wire: provides low-resistance path; keeps appliance body at earth potential, preventing severe shock.

  • Essential for metallic-body devices (toaster, press, refrigerator).

Illustrative calculation (Exercise 2)

• Oven: $P = 2\,\text{kW},\; V = 220\,\text{V}$

  • $I = P/V = 2000\text{ W}/220\text{ V} \approx 9.1\,\text{A}$ which exceeds $5\,\text{A}$ circuit rating → fuse blows / circuit breaker trips.

Magnetism in Medicine

• Nerve impulses ≈ ionic currents → produce magnetic fields $\sim10^{-9}$ T.

• Detectable fields from heart & brain exploited in MRI; allows non-invasive imaging for diagnosis.

Consolidated Key Concepts

• Compass needle aligns along local $\vec B$; north pole indicates field direction.

• Field lines: closed, non-intersecting; density ∝ $|\vec B|$.

• For straight conductor: $B \propto \frac{I}{r}$, direction via right-hand thumb rule.

• Circular coil: $B<em>{centre} \propto \frac{nI}{r}$ (exact expression involves $\mu</em>0$, beyond grade).

• Solenoid: nearly uniform internal field $B = \mu_0 n I$ (for long solenoid; $n$ = turns per unit length).

• Force on conductor: $\vec F = I\,\vec l \times \vec B$; magnitude $F = I l B \sin\theta$.

• Fleming’s left-hand vs right-hand rules:

  • Left-hand: predicts motor force (current & field known).

  • Right-hand (not detailed here) predicts induced current (generator effect).

• Domestic wiring colour code: Live – red, Neutral – black, Earth – green.

Important Formulas & Numerical Data

• Magnetic field around straight conductor (vacuum):
  $B = \frac{\mu_0 I}{2\pi r}$

• Force on current-carrying conductor in uniform $\vec B$:
  $\vec F = I (\vec l \times \vec B)$

• Joule heating in fuse/wire:
  $H = I^2 R t$

• AC mains (India): $V_{\text{rms}} = 220\,\text{V}$, frequency $f = 50\,\text{Hz}$.

Practice / Exam-Type Questions (derived from text)

• Draw magnetic field lines for:

  1. Bar magnet.

  2. Current-carrying circular loop (indicate inside & outside directions).

• Why can’t two field lines intersect?

• Describe three methods to increase the strength of an electromagnet.

• State precautions to avoid over-loading in domestic circuits.

• Using Fleming’s left-hand rule, give the force direction for a proton moving north in a field directed upward.