Courses
Courses for Kids
Free study material
Offline Centres
More
Store Icon
Store
seo-qna
SearchIcon
banner

The dimensional formula of k (Coulomb’s Constant) is _________. Take I as the dimension of current.
(A) M1L2T0I2
(B) M1L3T4I1
(C) M1L3T4I2
(D) M1L3T4I2

Answer
VerifiedVerified
149.7k+ views
like imagedislike image
Hint There can be two ways to approach the solution, first, if you know the dimensional formula of ε (permittivity of free space), just inverse the dimensional formula since the relation between k and ε is given as:
k=14πε
Other than that, you can use the relation between the force between two charged particles at rest, lying at a distance of r from each other with charges q1 and q2 . The relation is:
F=kq1q2r2
Take the dimensional formula of charge as: I1T1

Complete step by step answer
As explained in the hint section of the solution to the asked question, we will approach the solution by finding out the dimensional formula of Coulomb’s Constant using the relation between force, distance and charges.
The relation is given as:
F=kq1q2r2
As we already know, the SI unit of force is N and the dimensional formula is nothing but: [M1L1T2]
On the other hand, the dimensional formula of the distance, as the denominator term on the right-hand side, r is:
[L1]
The dimensional formula of charge is already told to be [I1T1]
Now, if we perform transposition in the equation, we get:
k=Fr2q1q2
Substituting the quantities with their dimensional formulae, we get;
k=[M1L1T2][L1]2[I1T1][I1T1]
If we simplify the above-mentioned term on the right-hand side of the equation, we get:
k=[M1L3T4I2]
Hence, the dimensional formula of k (Coulomb’s Constant) is: [M1L3T4I2]
As we can see, this matches with the dimensional formula given in the option (C). Hence,

option (C) is the correct answer to the question.

Note A major mistake that students make is that they take the dimension of charge exactly as I instead of I1T1 . Think of it as the equation of charge, Q=IT Where, Q is the charge passing through a particular cross-sectional area., I is the current flowing through the cross-sectional area and T is the time for which the current flowed through the cross-sectional area.
Latest Vedantu courses for you
Grade 11 Science PCM | CBSE | SCHOOL | English
CBSE (2025-26)
calendar iconAcademic year 2025-26
language iconENGLISH
book iconUnlimited access till final school exam
tick
School Full course for CBSE students
PhysicsPhysics
ChemistryChemistry
MathsMaths
₹41,848 per year
EMI starts from ₹3,487.34 per month
Select and buy