Question

The dimensional formula for the magnetic field is,

• A. $\left[M{T}^{-2}{A}^{-1}\right]$
• B. $\left[M{L}^2{T}^{-1}{A}^{-2}\right]$
• C. $\left[M{T}^{-2}{A}^{-2}\right]$
• D. $\left[M{T}^{-1}{A}^{-2}\right]$

Answer 1

The correct option is A

$\left[M{T}^{-2}{A}^{-1}\right]$

Step 1: Formula used for magnetic field

Magnetic field $=\frac{Force}{charge\times velocity}$

Step 2: Applying the dimensional formula

$\begin{array}{rcl}Force\left(F\right)& =& mass\left(m\right)\times acceleation\left(a\right)\\ & =& \left[M\right]\left[L{T}^{-2}\right]\\ & =& \left[ML{T}^{-2}\right]\end{array}$

$\left[Charge\right]=\left[AT\right]$

$\left[Velocity\right]=\left[L{T}^{-1}\right]$

Substituting the dimensions of the force, charge, and velocity,

$\begin{array}{rcl}& =& \frac{\left[ML{T}^{-2}\right]}{\left[AT\right]\left[L{T}^{-1}\right]}\\ & =& \left[M{T}^{-2}{A}^{-1}\right]\end{array}$

Therefore, the dimensional of the magnetic field $\left[M{T}^{-2}{A}^{-1}\right]$.

Hence, the correct option is A.