Answer to Question #218294 in Electricity and Magnetism for Anita

Question

Both epsilon 0 and Xe are dimensionless.

(a) True

(b) False

Answer 1

(1) $\epsilon_0$

Dimensions

$F=\frac{Kq_1q_2}{r^2}=\frac{q_1q_2}{4\pi \epsilon_0 r^2}$

$\epsilon_0=\frac{4\pi Fr^2}{q_1q_2}\rightarrow(1)$

Find dimensions

Put value equation (1)

$\epsilon_0=\frac{[M][LT^{-2}][L^2]}{[AT]^2}$

$\epsilon_0=[ML^3T^{-4}A^{-1}]$

$\epsilon_0$ Exist dimensions

(2)

$\chi$ dimensions

$\chi=\frac{M}{H}\rightarrow(2)$

equation (2) put value

H and M dimensions put find magnetic susceptibility dimensions

$\chi=[M^1L^1T^{-2}A^{-2}]$

$\chi$ exist dimensions

Both eqution exist dimensions

Statement are false

Option (b) is correct option