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1.Units, Dimensions and Measurement
medium
In terms of potential difference $V$, electric current $I$, permittivity $\varepsilon_0$, permeability $\mu_0$ and speed of light $c$, the dimensionally correct equation$(s)$ is(are)
$(A)$ $\mu_0 I ^2=\varepsilon_0 V ^2$ $(B)$ $\varepsilon_0 I =\mu_0 V$ $(C)$ $I =\varepsilon_0 cV$ $(D)$ $\mu_0 cI =\varepsilon_0 V$
A
$(B,D)$
B
$(B,C)$
C
$(A,C)$
D
$(A,D)$
(IIT-2015)
Solution
$BI \ell c \equiv VI \Rightarrow \mu_0 I ^2 c \equiv VI \Rightarrow \mu_0 Ic = V$
$\Rightarrow \mu_0^2 I ^2 c ^2= V ^2$
$\Rightarrow \mu_0 I ^2=\varepsilon_0 V ^2 \Rightarrow \varepsilon_0 cV = I$
Standard 11
Physics
