The dimension of magnetic field in $\mathrm{M}, \mathrm{L}, \mathrm{T}$ and C (Coulomb) is given as

(C) $\mathrm{MT}^{-1} \mathrm{C}^{-1}$

(A) $\mathrm{MLT}^{-1} \mathrm{C}^{-1}$

(B) $\mathrm{MT}^{2} \mathrm{C}^{-2}$

(D) $\mathrm{MT}^{-2} \mathrm{C}^{-1}$

JEE Main · 2008 · 27 Apr 2008 · Offline · Units & Measurement

The dimension of magnetic field in

M, L, T

and C (Coulomb) is given as

Answer: (C)

The quickest route to the dimensions of magnetic field is the Lorentz force law

F = q v B

, which rearranges to

B = \frac{F}{q v}

. Force carries dimensions

M L T^{- 2}

, charge carries

C

, and speed carries

L T^{- 1}

, so

[B] = \frac{M L T ^{- 2}}{C \cdot L T ^{- 1}}

. The length dimension cancels and a single power of time is left in the numerator, giving

[B] = M T^{- 1} C^{- 1}

as the dimensional formula of the magnetic field.

JEE Main · 2008 · 27 Apr 2008 · Offline · Single correct option