CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

What is the dimensional formula of the permittivity of a vacuum?


Open in App
Solution

Step 1: Definition

The substance's permittivity is a characteristic of all materials that quantifies the resistance to the production of an electric field.

The Greek alphabet ε is used to represent it. It indicates how many charges are necessary to create one unit of electric flux throughout the specified medium.

Farad/meter is the SI unit of permittivity.

Step 2: Dimensional formula

Since,

Force=[4πε]-1×[Charge2]×[Distance]-2

∴ Permittivity(ε)=[Charge2]×[Force]-1×[Distance]-2…(equation 1)

⇒Charge=current×time

∴ The dimensional formula of charge is:

[I1T1]…(equation 2)

The dimensional formula of distance is:

[M0L1T0] …(equation 3)

⇒Force=Mass×Acceleration

∴ The dimensional formula of force is:

[M1L1T-2] …(equation 4)

By substituting the values of equation 2,3, and 4 in equation 1 we get,

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

Or,

ε=[I1T1]2×[M1L1T-2]–1×[M0L1T0]-2=[M-1L-3T4I2]

Therefore, the dimensional formula of permittivity of vacuum will be [M-1L-3T4A2].


flag
Suggest Corrections
thumbs-up
3
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Gauss' Law Application - Infinite Line of Charge
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon