12.9 Magnetic Flux Density

Introduction

Magnetic flux density, also known as magnetic induction, is a fundamental concept in electromagnetism that measures the strength and direction of a magnetic field. It quantifies the force experienced by a current-carrying conductor placed within the magnetic field.

Magnetic Flux Density Formula

For a current-carrying conductor placed at right angles to a magnetic field, the magnetic flux density $B$ is calculated using the formula:

$B=\frac{F}{IL}$

Where:

• $F$ is the force acting on the conductor (in newtons, N)
• $I$ is the current in the conductor (in amperes, A)
• $L$ is the length of the conductor in the magnetic field (in meters, m)

Units of Magnetic Flux Density

The units used to measure magnetic flux density are Tesla in the SI system and Gauss in the CGS system. Since it is derived from other physical quantities, it is a Derived Unit→.

The conversion between these units is:

$1\text{T}=10^4\text{G}\text{or}1\text{G}=10^{-4}\text{T}$

Understanding a Tesla: If a 1-meter long conductor carrying a current of 1 A is placed perpendicular to a magnetic field and experiences a force of 1 N, then the magnetic flux density of that field is 1 Tesla (T).

Vector Nature of Magnetic Field

The magnetic field is a vector quantity, meaning it possesses both magnitude and direction.

• The magnitude of the magnetic flux density indicates the strength of the magnetic field.
• The direction is determined by the orientation of the magnetic field lines.

Scalar and Vector Quantities→

Dimensions of Magnetic Flux Density

Using the formula $B=\frac{F}{IL}$, we can determine the Dimensions→ of $B$: $[B]=\frac{[ML{T}^{-2}]}{[A][L]}=[M{T}^{-2}{A}^{-1}]$