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Question
Find the dimensions of magnetic field B.
The relevant equation are \[F = qE, F = qvB, \text{ and }B = \frac{\mu_0 I}{2 \pi a};\]
where F is force, q is charge, v is speed, I is current, and a is distance.
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Solution
Magnetic field,
\[B = \frac{F}{qv}\]
\[\text{ Here, } \left[ F \right] = {\left[ {MLT}^{- 2} \right]}, \left[ q \right] = {\left[ AT \right]} \text{ and } \left[ v \right] = {\left[ {LT}^{- 1} \right]} \]
\[\text{ So, dimension of magnetic field }, [B] = \frac{\left[ {MLT}^{- 2} \right]}{\left[ AT \right] \left[ {LT}^{- 1} \right]} = \left[ M L^0 T^{- 2} A^{- 1} \right]\]
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