Question

Drive dimensional formula of absilene zero mathematically​

Answer 1

Answer:

The dimensional formula for permittivity of free space (ϵ0) in the equation F=4πϵ01r2q1q2 where, symbols have their usual meaning is

Answer 2

The dimensional formula of Permittivity of free space or vacuum is given by,

M1 L-3 T4 I2

Where,

M = Mass

L = Length

T = Time

Derivation

Since, Force = [4πε]-1 × [Charge2] × [Distance]–2

∴ Permittivity (ε) = [Charge2] × [Force]–1 × [Distance]–2 . . . . . (1)

⇒ Charge = current × time

∴ The dimensional formula of charge = [I1 T1] . . . . . (2)

The dimensional formula of distance = [M0 L1 T0] . . . . . (3)

⇒ Force = Mass × Acceleration

∴ The dimensional formula of force = [M1 L1 T-2] . . . . . (4)

On substituting equation (2), (3) and (4) in equation (1) we get,

Permittivity = [Charge]2 × [Force]–1 × [Distance]–2

Or, ε = [I1 T1]2 × [M1 L1 T-2]–1 × [M0 L1 T0]–2 = [M1 L-3 T4 I2]

Therefore, the permittivity of free space or vacuum is dimensionally represented as M1 L-3 T4 I2.

Hope it helps you....✌️✌️