Question

The dimension of magnetic field in M, L, T and C (Coulomb) is given as:
A. \[ML{{T}^{-1}}{{C}^{-1}}\]
B. \[M{{T}^{2}}{{C}^{-2}}\]
C. \[M{{T}^{-1}}{{C}^{-1}}\]
D. \[ML{{T}^{-2}}{{C}^{-1}}\]

Answer 1

Hint: The dimensional formula of magnetic field can be calculated using the formula \[B=\dfrac{F}{qv}\] that has come from \[F=Bqv\]. This is the force acting on a charge q moving with velocity v in a magnetic field B.

Complete step by step answer:
To calculate the dimensional formula of magnetic field we take the formula
\[B=\dfrac{F}{qv}\]
This is the magnetic field B applied on a charge q, moving with a velocity v under the influence of a Magnetic Lorentz force F.
We must write each physical quantity used in its dimensional form:
Force F:
\[F=ma=[ML{{T}^{-2}}]\]
Charge q must be taken as Coulomb:
\[q=[C]\]
Velocity v:
\[v=[L{{T}^{-1}}]\]
Substituting these in the first equation we get:
\[B=\dfrac{[ML{{T}^{-2}}]}{[C][L{{T}^{-1}}]}\]
On solving we get:
\[B=[M{{T}^{-1}}{{C}^{-1}}]\]
Hence, the correct answer is option C. \[M{{T}^{-1}}{{C}^{-1}}\]
Additional Information:
The SI units and Dimensional formula of some important physical quantities to remember are:
Work, Energy of all kinds = \[J,[{{M}^{1}}{{L}^{2}}{{T}^{-2}}]\]
Power =\[W,[{{M}^{1}}{{L}^{2}}{{T}^{-3}}]\]
Planck’s Constant (h) = \[Js,[{{M}^{1}}{{L}^{2}}{{T}^{-1}}]\]
Angular displacement (\[\theta\])=$rad,[{{M}^{0}}{{L}^{0}}{{T}^{0}}]$.
Angular velocity (\[\omega\])=\[rad{{s}^{-1}}[{{M}^{0}}{{L}^{0}}{{T}^{0}}]\]
Force constant ($\dfrac{\text{force}}{\text{displacement}}$) = $N{{m}^{-1}},\left[ {{M}^{1}}{{L}^{0}}{{T}^{-2}} \right]$
Coefficient of elasticity ($\dfrac{\text{stress}}{\text{strain}}$) = $N{{m}^{-2}},\left[ {{M}^{1}}{{L}^{-1}}{{T}^{-2}} \right]$
Angular frequency \[(\omega )=,rad{{s}^{-1}}[{{M}^{0}}{{L}^{0}}{{T}^{-1}}]\]
Angular momentum \[I\omega =kg{{m}^{2}}{{s}^{-1}}[{{M}^{1}}{{L}^{2}}{{T}^{-1}}]\]

Note: Another method for solving this question would be by using the formula for force on a current carrying conductor placed in a magnetic field \[F=BIL\]and therefore, \[B=\dfrac{F}{IL}\] .While solving dimensional formula questions students must note that every physical quantity must be expressed in its absolute units only.