4. ELECTROMAGNETISM

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4. ELECTROMAGNETISM

Electromagnetism deals with the interaction between electric currents and magnetic fields. It explains how electric currents generate magnetic fields and how magnetic fields affect moving charges.

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4.1 Magnetic Field and Its Units

Magnetic Field (B):
A magnetic field is a region around a magnetic material or a moving charge in which the force of magnetism can be experienced by other magnetic materials or moving charges. It can be represented as lines that point from the north pole to the south pole of a magnet.

Units of Magnetic Field:

• The unit of the magnetic field is the Tesla (T) in the International System of Units (SI).
  • 1 Tesla = 1 Weber per square meter (Wb/m²).

Example: A magnetic field of 1 Tesla can exert a force of 1 newton on a 1-meter long conductor carrying a 1-ampere current perpendicular to the field.

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4.1.1 Magnetic Intensity (H)

• Magnetic Intensity (H) represents the strength and direction of the magnetic field produced by a current or a magnet. It’s related to the magnetic field $B$, but it focuses on the origin (like the current in a wire or the magnet itself).

• The relationship between magnetic field strength (B) and magnetic intensity (H) is given by:

  $$B = \mu H$$
  

  Where:

  • $B$ is the magnetic field (in Tesla).
  • $H$ is the magnetic intensity (in Ampere-turns per meter, At/m).
  • $\mu$ is the permeability of the material (in Henries per meter, H/m).

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4.1.2 Magnetic Lines of Force

• Magnetic Lines of Force are the invisible lines that represent the magnetic field around a magnet or a current-carrying conductor.
• These lines:
  1. Always form closed loops, either inside or outside the magnet.
  2. Start from the north pole of a magnet and end at the south pole.
  3. Never intersect.
  4. Are denser where the magnetic field is stronger.

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4.1.3 Magnetic Flux and Units

• Magnetic Flux (Φ_B):
  Magnetic flux represents the total magnetic field passing through a given area. It depends on the magnetic field strength and the area perpendicular to the field.

  $$\Phi_B = B \cdot A \cdot \cos(\theta)$$
  

  Where:

  • $\Phi_B$ is the magnetic flux.
  • $B$ is the magnetic field strength.
  • $A$ is the area through which the magnetic field lines pass.
  • $\theta$ is the angle between the magnetic field and the normal to the surface.

• Unit of Magnetic Flux:
  The SI unit of magnetic flux is the Weber (Wb).

  1 Weber = 1 Tesla × 1 square meter.

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4.2 Concept of Electromagnetic Induction

Electromagnetic Induction:
Electromagnetic induction occurs when a magnetic field changes in a conductor, inducing an electric current in that conductor. This principle is used in generators, transformers, and other devices.

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4.2.1 Faraday’s Laws and Lenz’s Law

Faraday’s Law of Induction:
Faraday's law states that the induced electromotive force (EMF) in a circuit is proportional to the rate of change of magnetic flux through the circuit:

$$\text{EMF} = - \frac{d\Phi_B}{dt}$$

Where:

• $\Phi_B$ is the magnetic flux.

• $\frac{d\Phi_B}{dt}$ is the rate of change of flux.

• The negative sign indicates that the induced EMF opposes the change in magnetic flux (this is the essence of Lenz’s Law).

Lenz’s Law:
Lenz’s law states that the direction of the induced current or EMF will be such that it opposes the change in the magnetic flux that produced it. This is a consequence of the law of conservation of energy.

Example: If a magnet is pushed toward a coil, the induced current will create a magnetic field that opposes the motion of the magnet.

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4.3 Magnetic Force on Moving Charge

• A charged particle moving in a magnetic field experiences a force, which is given by the Lorentz force law:

  $$F = q (v \times B)$$
  

  Where:

  • $F$ is the magnetic force.
  • $q$ is the charge of the particle.
  • $v$ is the velocity of the particle.
  • $B$ is the magnetic field.
  • $\times$ denotes the vector cross product (the direction of the force is perpendicular to both the velocity and magnetic field).

Example: A proton moving with a velocity of $10^6 \, \text{m/s}$ in a magnetic field of strength $0.1 \, \text{T}$ experiences a force. The charge of a proton is $1.6 \times 10^{-19} \, \text{C}$.

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4.3.1 Force on Current Carrying Conductor

• When a conductor carrying a current $I$ is placed in a magnetic field $B$, the conductor experiences a force given by:

  $$F = I \cdot L \cdot B \cdot \sin(\theta)$$
  

  Where:

  • $I$ is the current in the conductor.
  • $L$ is the length of the conductor.
  • $B$ is the magnetic field strength.
  • $\theta$ is the angle between the direction of the magnetic field and the current.

Example: If a wire carrying a current of 2 A is placed in a magnetic field of 0.5 T at an angle of 90°, and the length of the wire is 0.3 meters, the force on the wire is:

$$F = 2 \cdot 0.3 \cdot 0.5 = 0.3 \, \text{N}$$

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4.3.2 Force on Rectangular Coil Placed in Magnetic Field

• A rectangular coil placed in a magnetic field experiences a force and a torque. The force on each side of the coil is different depending on the orientation of the coil with respect to the magnetic field.

  The torque $\tau$ on a coil of area $A$ and carrying current $I$ in a magnetic field $B$ is given by:

  $$\tau = B \cdot A \cdot I \cdot \sin(\theta)$$
  

  Where:

  • $A$ is the area of the coil.
  • $I$ is the current through the coil.
  • $\theta$ is the angle between the normal to the coil and the magnetic field.

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4.4 Moving Coil Galvanometer: Principle, Construction, and Working

Moving Coil Galvanometer:
A moving coil galvanometer is an instrument used to measure small currents. It works on the principle that a current-carrying conductor placed in a magnetic field experiences a force.

• Construction:

  1. A coil of wire is suspended in a uniform magnetic field.
  2. The coil is mounted on a spindle, allowing it to rotate.
  3. A pointer is attached to the coil to indicate the current on a scale.

• Working: When a current passes through the coil, it experiences a force due to the magnetic field. This causes the coil to rotate, and the pointer moves across a scale to indicate the current.

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4.4.1 Conversion of a Galvanometer into Ammeter and Voltmeter

Ammeter:

• An ammeter is used to measure large currents.
• To convert a galvanometer into an ammeter, a shunt resistor (a very low resistance) is placed in parallel with the galvanometer to bypass most of the current, allowing the ammeter to measure larger currents without damaging the galvanometer.

Voltmeter:

• A voltmeter measures the potential difference across two points.
• To convert a galvanometer into a voltmeter, a high resistance is placed in series with the galvanometer to limit the current, allowing it to measure small voltage differences without damaging the instrument.

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Summary of Key Concepts:

• Magnetic Field (B): The region where magnetic forces are felt.
• Magnetic Intensity (H): The strength and direction of the magnetic field.
• Faraday's and Lenz's Laws: Describe how a changing magnetic field induces current and the direction of the induced EMF.
• Magnetic Force on Charges: Moving charges experience a force in a magnetic field.
• Ammeter and Voltmeter Conversion: A galvanometer can be converted into an ammeter or voltmeter by using appropriate resistances.

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Numerical Example on Magnetic Force:

Problem: A current of 5 A flows through a conductor of length 0.4 m placed in a magnetic field of strength 0.6 T. The angle between the field and the conductor is 90°. What is the force on the conductor?

Solution: Using the formula for force on a current-carrying conductor:

$$F = I \cdot L \cdot B \cdot \sin(\theta)$$

Substitute the given values:

$$F = 5 \cdot 0.4 \cdot 0.6 \cdot \sin(90^\circ)$$
$$F = 5 \cdot 0.4 \cdot 0.6 = 1.2 \, \text{N}$$

Answer: The force on the conductor is 1.2 N.

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