Question

What is the dimension of k in coulomb's law basic equation F=kq1q2/r2

Answer 1

F=kq1q2/R2

F×R^2/q1q2=K

MLT^-2×L^2/A^2T^2=K

ML^3T^0A=K

Answer 2

Answer:

$\boxed{\mathfrak{[k] = [ML ^{3} T^{-4}A ^{ - 2}}}$

Explanation:

From Coulomb's Law:

$\rm \implies F = \dfrac{kq_1q_2}{r^2} \\ \\ \rm \implies k = \dfrac{F {r}^{2} }{q_1q_2}$

Dimensional formula:

$\rm [F] =[MLT^{-2}] \\ \rm [q] = [AT] \\ \rm [r] = [L]$

So, dimensional formula of Coulomb's constant (k) is:

$\rm \implies [k] = \dfrac{[F][r]^2}{[q]^2} \\ \\ \rm \implies [k] = \frac{ [MLT^{-2}][L] ^{2} }{[AT] ^{2} } \\ \\ \rm \implies [k] = \frac{ [MLT^{-2}][L ^{2} ] }{[A ^{2} T ^{2} ] } \\ \\ \rm \implies [k] = [ML ^{1 + 2} T^{-2 - 2}A ^{ - 2}] \\ \\ \rm \implies [k] = [ML ^{3} T^{-4}A ^{ - 2}]$