Electric displacement is given by D = εE here, ε = electric permittivity, E = electric field strength. The dimensions of electric displacement are

• [M L⁻² T⁻² A]
• [L⁻² T⁻¹ A]
• [L⁻² T⁻² A]
• None of these

To find the dimensions of electric displacement (D), we start with the formula D = εE, where ε is the electric permittivity and E is the electric field strength.

Breaking Down the Components

First, let's analyze the dimensions of each component:

• Electric Permittivity (ε): The dimensions of ε are [M⁻¹ L⁻³ T⁴ A²].
• Electric Field Strength (E): The dimensions of E are [M L⁻² T⁻² A⁻¹].

Calculating the Dimensions of D

Now, we can combine these dimensions to find D:

D = εE = [M⁻¹ L⁻³ T⁴ A²] × [M L⁻² T⁻² A⁻¹]

When we multiply these, we get:

• Mass (M): M⁻¹ × M = M⁰ = 1
• Length (L): L⁻³ × L⁻² = L⁻⁵
• Time (T): T⁴ × T⁻² = T²
• Current (A): A² × A⁻¹ = A¹

Final Dimensions

Putting it all together, the dimensions of electric displacement (D) are:

[L⁻⁵ T² A]

Therefore, the correct answer is None of these, as the provided options do not match the calculated dimensions.