Question

Find the dimensions of the following
i. Power ii. Forceiii. Electric Permittivity

Answer 1

Explanation:

Power - M^1L^2T^-3

Force - M^1L^1T^-2

Electric permittivity -M^-1L^-3T^4A^2

Answer 2

power is energy consumed per unit time. i.e., Power = energy/time

and energy = workdone by particle = Force × displacement

and force = mass × acceleration.

we know,

• dimension of acceleration = [LT-²]
• dimension of mass = [M]
• dimension of time = [T]
• dimension of displacement = [L]

so, dimension of force = dimension of mass × dimension of force

= [M] × [LT-²]

= [MLT-²]

dimension of power = dimension of energy/dimension of time

= dimension of force × dimension of displacement/[T]

= [MLT-²] × [L]/[T]

= [ML²T-³]

dimension of electric permittivity can't be found directly.

let's see Coulomb's force, F = qQ/4π∈r²

here, ∈ is electric permittivity.

so, dimension of ∈ = dimension of qQ/dimension of F × dimension of r²

= [AT]²/[MLT-²] × [L²]

[ dimension of charge = [AT], so, dimension of qQ = dimension of charge ² = [AT]²]

= [M-¹L-³T⁴A²]

hence, dimension of electric permittivity = [M-¹L-³T⁴A²]