Dimensional analysis of permittivity of vaccum
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We want the dimensional formula for absolute permittivity.
F=14πϵ0⋅q1q2r2⇒ϵ0=14πF⋅q1q2r2.F=14πϵ0⋅q1q2r2⇒ϵ0=14πF⋅q1q2r2.
The dimensions of F,q1,q2F,q1,q2 and rr are MLT−2,AT,ATMLT−2,AT,AT and LL respectively.
⇒⇒ The dimensions of ϵ0ϵ0 are (AT)2MLT−2.L2=M−1L−3T4A2,(AT)2MLT−2.L2=M−1L−3T4A2,
where M,L,TM,L,T and AA are the dimensions of mass, length, time and current respectively.
F=14πϵ0⋅q1q2r2⇒ϵ0=14πF⋅q1q2r2.F=14πϵ0⋅q1q2r2⇒ϵ0=14πF⋅q1q2r2.
The dimensions of F,q1,q2F,q1,q2 and rr are MLT−2,AT,ATMLT−2,AT,AT and LL respectively.
⇒⇒ The dimensions of ϵ0ϵ0 are (AT)2MLT−2.L2=M−1L−3T4A2,(AT)2MLT−2.L2=M−1L−3T4A2,
where M,L,TM,L,T and AA are the dimensions of mass, length, time and current respectively.
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