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Question
Find the dimensions of electric field E.
The relevant equations 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
Electric field is defined as electric force per unit charge.
i.e., \[E = \frac{F}{q}\]
\[\text{ Also,} \left[ F \right] = {\left[ {MLT}^{- 2} \right]} \text{ and } \left[ q \right] ={\left[ AT \right]}\]
\[\text{ So, dimension of electric field }, [E] = \left[ {MLT}^{- 3} A^{- 1} \right]\]
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