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 $$B={\displaystyle \frac{F}{qv}}$$ 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
$$B={\displaystyle \frac{F}{qv}}$$
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:
$$B={\displaystyle \frac{[ML{T}^{-2}]}{[C][L{T}^{-1}]}}$$
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 (${\displaystyle \frac{\text{force}}{\text{displacement}}}$) = $N{m}^{-1},\left[M^1{L}^0{T}^{-2}\right]$
Coefficient of elasticity (${\displaystyle \frac{\text{stress}}{\text{strain}}}$) = $N{m}^{-2},\left[M^1{L}^{-1}{T}^{-2}\right]$
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, $$B={\displaystyle \frac{F}{IL}}$$ .While solving dimensional formula questions students must note that every physical quantity must be expressed in its absolute units only.