The dimension of the magnetic field intensity | vedclass

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Question

(B) The magnetic force $F$ on a current-carrying conductor of length $l$ carrying current $i$ in a magnetic field $B$ is given by $F = Bil \sin 	heta

Vedclass · Accepted Answer

$M{T^{ - 2}}{A^{ - 1}}$

Vedclass · Answer

(B) The magnetic force $F$ on a current-carrying conductor of length $l$ carrying current $i$ in a magnetic field $B$ is given by $F = Bil \sin 	heta$.Taking the magnitude,we have $F = Bil$.Rearranging for $B$,we get $B = \frac{F}{il}$.The dimensional formula for force $F$ is $[F] = MLT^{-2}$.The dimensional formula for current $i$ is $[i] = A$.The dimensional formula for length $l$ is $[l] = L$.Substituting these into the expression for $B$:$[B] = \frac{[F]}{[i][l]} = \frac{MLT^{-2}}{A \cdot L} = MT^{-2}A^{-1}$.Thus,the correct option is $B$.

The dimension of the magnetic field intensity $B$ is

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