Concepts Of Physics MCQ Edition [Volume 2]PhysicsElectric Field and Potential
Determine the dimensional formula of ₀ .
Options
- AM⁻¹ L⁻³ T^4 I^2
- BM L^3 T⁻⁴ I^ -2
- CM⁻¹ L⁻³ T^3 I
- DM⁻¹ L⁻² T^4 I^2
Correct answer
A. M⁻¹ L⁻³ T^4 I^2
Step-by-step solution
Using Coulomb's law: F = 1 4 ₀ q₁ q₂ r^2 Rearranging for ₀ : ₀ = q₁ q₂ 4 F r^2 Substituting the dimensional formulas for charge [q] = I T , force [F] = M L T⁻² , and distance [r] = L : [ ₀] = [I T] [I T] [M L T⁻²] [L^2] [ ₀] = I^2 T^2 M L^3 T⁻² [ ₀] = M⁻¹ L⁻³ T^4 I^2