Question #218294

Both epsilon 0 and Xe are dimensionless.

(a) True

(b) False


1
Expert's answer
2021-07-21T08:34:01-0400

(1) ϵ0\epsilon_0

Dimensions

F=Kq1q2r2=q1q24πϵ0r2F=\frac{Kq_1q_2}{r^2}=\frac{q_1q_2}{4\pi \epsilon_0 r^2}

ϵ0=4πFr2q1q2(1)\epsilon_0=\frac{4\pi Fr^2}{q_1q_2}\rightarrow(1)

Find dimensions

Put value equation (1)

ϵ0=[M][LT2][L2][AT]2\epsilon_0=\frac{[M][LT^{-2}][L^2]}{[AT]^2}

ϵ0=[ML3T4A1]\epsilon_0=[ML^3T^{-4}A^{-1}]

ϵ0\epsilon_0 Exist dimensions

(2)

χ\chi dimensions

χ=MH(2)\chi=\frac{M}{H}\rightarrow(2)

equation (2) put value

H and M dimensions put find magnetic susceptibility dimensions

χ=[M1L1T2A2]\chi=[M^1L^1T^{-2}A^{-2}]

χ\chi exist dimensions

Both eqution exist dimensions

Statement are false

Option (b) is correct option



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