Dimensions of magnetic field intensity is: [PMT/NEET-1997]
a. $[M^{0}L^{-1}T^{0}A^{1}]$
b. $[MLT^{-1}A^{-1}]$
c. $[ML^{0}T^{-2}A^{-1}]$
d. $[MLT^{-2}A]$
Solution
Use Lorentz force on a current element:
$F = B\,I\,L \Rightarrow B = \dfrac{F}{I\,L}$.
Dimensions: $[F]=MLT^{-2}$,
$[I]=A$,
$[L]=L$.
Hence $[B]=\dfrac{MLT^{-2}}{A\cdot L}=MT^{-2}A^{-1}$,
i.e. $[M^{1}L^{0}T^{-2}A^{-1}]$.
Answer
c. $[ML^{0}T^{-2}A^{-1}]$