Question

The magnetic field dimensions in M, L, T, and C (coulomb) are given as

• A. $\left[{\mathrm{MLT}}^{-1}{\mathrm{C}}^{-1}\right]$
• B. $\left[{\mathrm{MT}}^2{\mathrm{C}}^{-2}\right]$
• C. $\left[{\mathrm{MT}}^{-1}{\mathrm{C}}^{-1}\right]$
• D. $\left[{\mathrm{MT}}^{-2}{\mathrm{C}}^{-1}\right]$

Answer 1

The correct option is C

$\left[{\mathrm{MT}}^{-1}{\mathrm{C}}^{-1}\right]$

1. Force F acting on charge q moving with velocity v in magnetic field B is given by the formula $F=QvB$ where, $Q$ is a charge, $B$ is the magnetic field, and $v$ is the velocity.
2. The dimension of force is $\left[{\mathrm{MLT}}^{-2}\right]$.
3. The dimension of charge is $\left[\mathrm{C}\right]$.
4. The dimension of velocity is $\left[{\mathrm{LT}}^{-1}\right]$.
5. The dimension of the magnetic field can be calculated as-

$\begin{array}{rcl}F& =& QvB\\ \left[{\mathrm{MLT}}^{-2}\right]& =& \left[\mathrm{C}\right]\left[{\mathrm{LT}}^{-1}\right]\left[\mathrm{B}\right]\\ \left[\mathrm{B}\right]& =& \left[{\mathrm{MC}}^{-1}{\mathrm{T}}^{-1}\right]\end{array}$

Hence, option C is the correct answer.