Magnetic Fields

(a) Determining the Direction of Force on a Current-Carrying Conductor in a Magnetic Field

Use Fleming’s Left-Hand Rule:

  • Thumb: Direction of Force (Motion)

  • First Finger: Direction of Magnetic Field (B)

  • Second Finger: Direction of Current (I)

Force is perpendicular to both the current and magnetic field.

(b) Calculating the Magnetic Field (B) Using Force on a Current-Carrying Conductor

The force experienced by a conductor in a magnetic field is given by:

F = BIl sin Θ

Where:

  • F = Force (N)

  • B = Magnetic Field Strength (T)

  • I = Current (A)

  • l = Length of Conductor in Field (m)

  • Θ = Angle between current and magnetic field

If the conductor is perpendicular to the field, sin 90° = 1, and the maximum force is exerted.

(c) Using F = Bqv sinΘ for a Moving Charge in a Magnetic Field

A charged particle moving in a magnetic field experiences a force:

F = Bq vsinΘ

Where:

  • q = Charge (C)

  • v = Velocity of Particle (m/s)

If the particle moves perpendicular to B, sin 90° = 1, and the force is maximum, causing circular motion.

(d) Production of Hall Voltage and VH ∝ B for Constant I

When a current flows through a conductor in a perpendicular magnetic field, charge carriers experience a force and accumulate on one side, creating a potential difference (Hall Voltage, VH).

Hall Voltage is proportional to Magnetic Field Strength (B) for constant I:

VH ∝ B

This principle is used in Hall effect sensors to measure magnetic fields.

(e) Shapes of Magnetic Fields

Long Straight Wire: Concentric circles around the wire (Right-Hand Grip Rule).

Long Solenoid: Field lines inside are uniform and resemble a bar magnet (strongest inside).

(f) Magnetic Field Strength Equations

Long Straight Wire: B = μ0I / 2𝛑a

  • a = Distance from wire

Long Solenoid: B = μ0 nI

  • n = Number of turns per unit length

(g) Effect of an Iron Core in a Solenoid

Adding an iron core increases magnetic permeability, concentrating the field lines and significantly increasing B.

(h) Forces Between Current-Carrying Conductors

Parallel conductors with current in the same direction attract, opposite directions repel.

Key Points on Forces Between Parallel Conductors

  1. Attractive Force: Two parallel conductors carrying current in the same direction experience an attractive force due to their magnetic fields.

  2. Net Force Calculation: If currents are equal and steady, forces on conductors are equal in magnitude but opposite in direction, resulting in a net force of zero externally.

  3. Repulsive Force: If currents flow in opposite directions, the magnetic fields create repulsive forces, leading to a net force away from each other.

  4. Equilibrium Condition: Equal currents lead to cancellation of attractive forces, keeping the system in equilibrium when viewed externally.

(i) Deflection of Ion Beams in Uniform Electric and Magnetic Fields

  • Electric Field: Force is linear (qE).

  • Magnetic Field: Force is perpendicular (qvB) and causes circular motion.

  • Lorentz Force: Combination of electric and magnetic forces.

(j) Motion of Charged Particles in Accelerators

  • Linear Accelerators: Alternating electric fields accelerate charged particles.

  • Cyclotrons: Circular acceleration using perpendicular B-field.

  • Synchrotrons: Adjusted magnetic fields keep particles in circular paths while increasing speed.

Sketching the Direction of Force Using Fleming's Left-Hand Rule

To sketch the direction of force on each wire in a magnetic field:

  1. Identify the Directions: Determine the direction of the current (I) through

    the wire and the direction of the magnetic field (B).

  2. Apply Fleming’s Left-Hand Rule: Position your left hand so that:

    • Your First Finger points in the direction of the Magnetic Field (B).

    • Your Second Finger points in the direction of the Current (I).

    • Your Thumb will then point in the direction of the Force (Motion).

  3. Draw the Vectors: Sketch arrows to represent the direction of the Magnetic Field, Current, and resulting Force on the wire.

Remember, the force is always perpendicular to both the magnetic field and the direction of current.

Effects of changing relative permittivity

The insulator between current-carrying wires affects the magnetic field based on its relative permeability:

Relative Permeability < 1. The material is less permeable than vacuum, decreasing magnetic field strength in the region between the wires, reducing magnetic coupling.

Relative Permeability = 1: No effect from insulators; behaves like vacuum, magnetic field can propagate normally

Relative Permeability > 1: (like ferromagnetic materials), Enhances magnetic field strength, concentrating field lines, increasing the field experienced

Magnetic coupling refers to the interaction between magnetic fields of current-carrying conductors or permanent magnets, which affects the strength and direction of the magnetic field experienced in nearby regions.

It is influenced by factors such as the relative permeability of the materials involved.