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Magnetic Field, Definition, Magnetic Force, Characteristics Of Magnetic Force

Magnetic Field : Uncover the fascinating world of Magnetic Fields and Magnetic Forces. Learn how these powerful phenomena shape our understanding of electromagnetism and its applications. Explore the concepts and implications behind magnetic fields and discover the intriguing forces they exert.
authorImageShrivastav 10 Jan, 2024
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Magnetic Field

Magnetic Field : The concept of a magnetic field and magnetic force is fundamental to understanding the behavior of magnets and their interaction with other magnetic materials.

Magnetic Field

Magnetic Field : A magnetic field is an area of space where charged particles and magnetic materials experience magnetic forces.

It is produced by moving electric charges or by the intrinsic magnetic moments of elementary particles such as electrons.
  • Symbol - B
  • Unit - Tesla
  • Direction - Represent by Magnetic Field Lines

Magnetic Field Lines

Magnetic field lines are imaginary lines that are used to depict the strength and direction of a magnetic field.
  • They are a visual tool to understand the behavior of magnetic fields
  • The magnetic field's strength is represented by the density of the magnetic field lines.
  • Magnetic field lines don't ever overlap or intersect one another.
  • Magnetic field lines form closed loops within a magnet, indicating that the magnetic field is continuous.

Magnetic Force

The magnetic force is the force exerted on a moving charged particle or a current-carrying conductor in a magnetic field. When a charged particle, such as an electron, moves through a magnetic field, it experiences a force that is perpendicular to both its velocity and the magnetic field direction. The equation yields this force:

F = qvBsinθ

Where:
  • F = Magnitude of the magnetic force
  • q = Charge of the particle
  • v = Velocity of the particle
  • B = Magnetic field strength
  • θ = Angle between the velocity vector and the magnetic field vector

Characteristics of Magnetic Force

  • There is no magnetic force acting on a stationary charge in a magnetic field.
  • A moving charge experiences no magnetic force when it moves parallel or antiparallel to the magnetic field direction.
  • The maximum magnetic force is exerted on a moving charge when it moves perpendicular to the magnetic field direction.

Magnetic Field of a Straight Line Current

The magnetic field produced by a straight line current can be calculated using Ampere's law. When the magnetic field (B) at a specific location surrounding a conductor that carries current is inversely proportional to the conductor's distance (r) and directly proportional to the current (I). For a straight line current, the magnetic field can be calculated using the formula:

B = μ 0 / 2πr

Where,
  • B = Magnetic field strength
  • μ 0 = Permeability of free space
  • I = Current flowing through the conductor
  • r = Distance from the conductor

Magnetic Field Variation on The Radial Distance

To derive the variation of the magnetic field on the radical distance from a current-carrying wire, you can use Ampere's law in integral form. According to Ampere's law, the magnetic field surrounding a closed loop is proportional to the current flowing through it. Consider a long straight wire carrying a current I. We want to determine how the magnetic field (B) varies with the radical distance (r) from the wire.

We start by defining a circular loop of radius r centered on the wire. Ampere's law states that the magnetic field's line integral (∮B⋅dl) around this closed loop is equal to the sum of the loop's current and the permeability of empty space (μ 0 ). B.dl = μ 0 I For a long straight wire, the magnetic field is purely circular and has the same magnitude at every point along the circular loop. Therefore, the dot product of the magnetic field and the differential length dl simplifies to Bdl. The formula for the magnetic field at a point is given as - B = (μ₀I) / (2πr) Where, B is the magnetic field strength, μ₀ is the permeability of free space (a constant value), I is the current in the wire, and r is the radial distance from the wire. From the formula, we can observe that the magnetic field strength (B) is inversely proportional to the axial distance (r). This means that as you move farther away from the wire along its axis, the magnetic field strength decreases. In other words, the magnetic field becomes weaker with increasing radial distance .

Magnetic Field of a Current-carrying Circular Loop

The magnetic field produced by a current-carrying circular loop can be calculated using the Biot-Savart law. According to the Biot-Savart law, the magnetic field at a point due to a small current element is given by

dB = μ 0 4 (IdLxr/r3)

Where , dB = Magnetic field vector at the point of observation.

μ 0 =Permeability of free space

I = Current flowing through the loop. dL = Differential length element of the loop. r = position vector

For a circular loop, we can divide it into multiple small current elements dl and integrate the contributions of each element to find the total magnetic field at a point. However, there is a special case where we can find a simpler expression for the magnetic field at the center of the loop. This occurs when the loop is symmetrically placed, and the point of observation is at the center of the loop. In this case, the magnetic field at the center of the loop can be calculated as: B = μ 0 IR / 2R 2 = (μ0/2R) B = Magnitude of the magnetic field at the center of the loop. R = Radius of the loop.

Magnetic Field of a Solenoid

A solenoid is a coil of wire that is often wrapped around a cylindrical core. When an electric current passes through the wire, it generates a magnetic field inside the solenoid. The magnetic field of a solenoid is described by the following formula:

B = μ 0 IN / L

Where, N = Number of turns in the solenoid I = Current in the coil L = Length of the coil.

Magnetic Field FAQs

Q1. What is a magnetic field?

Ans. A magnetic field is a region of space around a magnet or a current-carrying conductor where magnetic forces are exerted on other magnets or moving charges. It is represented by magnetic field lines that indicate the direction and strength of the magnetic field.

Q2. How is a magnetic field created?

Ans. A magnetic field is created by the motion of electric charges. It can be generated by permanent magnets, electric currents flowing through wires, or even by the movement of charged particles, such as electrons, within atoms.

Q3. What is the unit of measurement for magnetic field strength?

Ans. The unit of measurement for magnetic field strength is the tesla (T), named after Nikola Tesla. Another commonly used unit is the gauss (G), with 1 T equal to 10,000 G.

Q4. What is the difference between a magnetic field and an electric field?

Ans. The main difference between a magnetic field and an electric field is their source. A magnetic field is produced by moving charges, whereas an electric field is created by stationary or moving charges. Additionally, electric fields exert forces on stationary charges, while magnetic fields exert forces on moving charges or other magnets.

Q5. How can the magnitude of the magnetic force be calculated?

Ans. The magnitude of the magnetic force on a moving charged particle can be calculated using the equation: F = qvBsinθ, where F is the magnetic force, q is the charge of the particle, v is its velocity, B is the magnetic field strength, and θ is the angle between the velocity and the magnetic field.
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