In Physics, an Electric Field is the region of space around a charged particle where a force would be exerted on other charged particles. Calculating its dimensional formula is a standard problem in Class 11 Mechanics.
The SI unit of the Electric Field is Newton per Coulomb (N/C) or Volts per meter (V/m).
Dimensional analysis helps to check whether a derived physics equation is dimensionally correct (homogeneity).
To find the dimension, we start with the fundamental definition of the Electric Field ($E$). Electric field is defined as the Electrostatic Force ($F$) experienced per unit Charge ($q$). Formula: $E = \frac{F}{q}$
Now, we need the dimensional formulas for Force and Charge.
Substitute these back into the base formula: $E = \frac{[M^1 L^1 T^{-2}]}{[A^1 T^1]}$
Now, bring the denominator terms to the top (which changes the sign of their exponents): $E = [M^1 L^1 T^{-2}] \times [A^{-1} T^{-1}]$
Combine the Time ($T$) terms ($-2 - 1 = -3$): Final Dimensional Formula = $[M^1 L^1 T^{-3} A^{-1}]$
The 'A' stands for Ampere, which is the fundamental SI unit for electric current. (Some textbooks use 'I' instead of 'A', making the formula $[M^1 L^1 T^{-3} I^{-1}]$).
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