Q.

In terms of potential difference  V, electric current I,  permittivity ε0,  permeability  μ0 and speed of light c,  the dimensionally correct equation(s) is (are)

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a

μ0I2=ε0V2

b

ε0I=μ0V

c

I=ε0cV

d

μ0cI=ε0V

answer is A.

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Detailed Solution

Dimensional formula,V=ML2T−3A−1I=[A]ε0=M−1L−3T4A2μ0=MLT−2A−2c=∠T−1Option A:LHS=μ02=MLT−2A−2[A]2=MLT−2RHS=ε0V2=M−1L−3T4A2ML2T−3A−12=MLT−2 Correct. Option B:LHS=ε0I=M−1L−3T4A2[A]=M−1L−3T4A3RHS=μ0V=MLT−2A−2ML2T−3A−1=M2L3T−5A−3 Incorrect. Options C:LHS=I=[A]RHS=ε0cV=M−1L−3T4A2LT−1ML2T−3A−1=[A] Correct. Option D:LHS=μ0cl=MLT−2A−2LT−1[A]=ML2T−3A−1RHS=ε0V=M−1L−3T4A2ML2T−3A−1=M0L−1TA Incorrect.
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