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Question

The dimensional formula for the magnetic fields is

A
$$ [ML^2T^{-1}A^{-2} ] $$
B
$$ [MT^{-1} A^{-2}] $$
C
$$ [MT^{-2}A^{-2}] $$
D
$$ [MT^{-2} A^{-1} ] $$
Solution
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Correct option is A. $$ [MT^{-2} A^{-1} ] $$
We have the equation,

$$F=qvB\,sin\theta$$

Dimension of Force, $$F=[MLT^{-2}]$$

Dimension of Velocity, $$v=[LT^{-1}]$$

Dimension of Charge, $$q=[AT]$$

$$Sin\theta $$ is dimensionless

Then,

Magnetic Field, $$B=\dfrac{Force}{Velocity \times Charge}=\dfrac{[MLT^{-2}]}{[LT^{-1}][AT]}=[MT^{-2}A^{-1}]$$

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