Question

The dimensions of a magnetic field in $M$,$L$,$T$ and$C$ (Coulomb) are given as,
A. $\left[ {ML{T^{ - 1}}{C^{ - 1}}} \right]$
B. $\left[ {M{T^{ - 2}}{C^{ - 2}}} \right]$
C. $\left[ {M{T^{ - 1}}{C^{ - 1}}} \right]$
D. $\left[ {M{T^{ - 2}}{C^{ - 1}}} \right]$

Answer 1

Hint: The primary dimensions are mass [M], length [L], time [T] and current [I]. Coulomb[C] is
a dimension derived from the primary dimension. To find the dimension of magnetic field, the
Lorentz force formula has to be known which is given as, $\left| {\overrightarrow F } \right| =
\left| {q\overrightarrow v \times \overrightarrow B } \right|$. The Lorentz force is a force
exerted on a charged particle q moving with a velocity v in a magnetic field. The direction of this
field is given by Fleming’s right hand rule.
Complete step by step solution:
Using the Lorentz force formula, the magnetic field can be derived.
We know that, force is mass multiplied by its acceleration, $F = ma$
The dimension of force is given as,
$\left[ F \right] = \left[ {ML{T^{ - 2}}} \right]$ ……(1)
The dimension of charge, q is,
$\left[ q \right] = \left[ C \right]$
The dimension of velocity is,
$\left[ v \right] = \left[ {L{T^{ - 1}}} \right]$ ……(2)
The equation of magnetic field from Lorentz force formula is,
$B = \dfrac{F}{{qv}}$ ……(3)
Here, q is the charge and v is the velocity of charge.
Hence, the dimension of magnetic field is calculated by substituting the dimensions of F, q and v
from equation (1) and equation (2) in equation (3),
$B = \dfrac{{\left[ {ML{T^{ - 2}}} \right]}}{{[C][L{T^{ - 1}}]}} = [M{T^{ - 1}}{C^{ - 1}}]$
Hence the correct answer is (C).
Note: the students have to apply the concept of primary dimensions and derived dimensions. The
formula for magnetic field calculation has to be identified. The derived dimension has to be

obtained in terms of the primary dimensions, M, L, T and C. Using Lorentz force formula; the
magnetic field can be obtained. Each parameter has to be expressed in terms of M, L, T and C in
order to obtain its dimension.