Question

Write the dimensional formula of magnetic induction.

Answer 1

Magnetic induction:

1. When a charged particle is moving, it experiences a force that is usually defined as the magnetic flux intensity or magnetic field, or magnetic induction.
2. It was discovered by Michael Faraday in 1831
3. The S.I unit of magnetic induction or magnetic field $\left(B\right)$ is tesla $\left(T\right)$.

Dimensional formula of magnetic induction:

1. Lorentz force is defined as the combination of the magnetic and electric force on a point charge due to electromagnetic fields. It is used in electromagnetism and is also known as the electromagnetic force. It can be expressed as,

$\mathrm{Lorentz}\mathrm{Force}\left(F\right)=\mathrm{Charge}\times \mathrm{Magnetic}\mathrm{Field}\left(B\right)\times \mathrm{Velocity}$

2. The mathematical expression for velocity is,

$\mathrm{Velocity}=\mathrm{Distance}\times {\mathrm{Time}}^{-1}$

3. The mathematical expression for an electric charge is,

$\mathrm{Electric}\mathrm{charge}=\mathrm{electric}\mathrm{current}\times \mathrm{time}$

4. The dimension for Lorentz force are as follows:

$\mathrm{Force}=\mathrm{Mass}\times \mathrm{Acceleration}=M\times [L{T}^{-2}]$

5. The dimensional for Magnetic induction $\left(B\right)$ is given as,

$\mathrm{Magnetic}\mathrm{Field}\left(\mathrm{B}\right)=\mathrm{Lorentz}\mathrm{Force}\times {[\mathrm{Charge}\times \mathrm{Velocity}]}^{-1}$

$B=[ML{T}^{-2}]\times {[AT]}^{-1}\times {[L{T}^{-1}]}^{-1}=[M^1{L}^0{T}^{-2}{A}^{-1}].$

Hence, the dimensional formula of magnetic Induction is $\left[{\mathrm{M}}^1{\mathrm{L}}^0{\mathrm{T}}^{-2}{\mathrm{A}}^{-1}\right]$.