The dimensional formula of electric flux is [M¹ L³ T⁻³ I⁻¹].
Let's break down how we arrive at this formula.
Electric flux (ΦE) is defined as the electric field (E) multiplied by the area (A) through which the field passes:
ΦE = E ⋅ A
Therefore, to find the dimensional formula of electric flux, we need to know the dimensional formulas of electric field and area.
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Area (A): Area is length squared. Therefore, the dimensional formula of area is [L²].
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Electric Field (E): Electric field is defined as force (F) per unit charge (q): E = F/q.
- Force (F): According to Newton's second law, force is mass times acceleration (F=ma). The dimensional formula of force is [M¹ L¹ T⁻²].
- Charge (q): Charge is current (I) multiplied by time (t): q = It. Therefore, the dimensional formula of charge is [I¹ T¹].
Therefore, the dimensional formula of the electric field is:
E = F/q = [M¹ L¹ T⁻²] / [I¹ T¹] = [M¹ L¹ T⁻³ I⁻¹].
Now, we can find the dimensional formula of electric flux:
ΦE = E ⋅ A = [M¹ L¹ T⁻³ I⁻¹] ⋅ [L²] = [M¹ L³ T⁻³ I⁻¹]
Therefore, the dimensional formula for electric flux is indeed [M¹ L³ T⁻³ I⁻¹].
