Where = magnetising intensity; = electric field; = permittivity, = distance, = time. The values of and respectively are [2026]

Question

Consider the equation $H = \frac{x^{p} ε^{q} E^{r}}{t^{s}}$

Where $H$ = magnetising intensity; $E$ = electric field; $ε$ = permittivity, $x$ = distance, $t$ = time. The values of $p, q, r$ and $s$ respectively are [2026]

Smart Achievers · Accepted Answer

(1)

$As per problem if we take H as magnetic field then no option matching but if we take H as magnetising intensity instead of magnetic field then only we get answer$

$H = \frac{B}{μ_{0}} - N i \Rightarrow current per unit length$

$\Rightarrow [H] = [A L^{- 1}]$

$[E] = \frac{[M L T^{- 2}]}{[I T]} = [M L A^{- 1} T^{- 3}]$

$[ε] = \frac{[I^{2} T^{2}]}{[M L T^{- 2} L^{2}]} = [M^{- 1} L^{- 3} I^{2} T^{4}]$

$H = \frac{x^{p} ε^{q} E^{r}}{t^{s}}$

$A L^{- 1} = \frac{L^{p} {(M^{- 1} L^{- 3} T^{4} A^{2})}^{q} {(M L T^{- 3} A^{- 1})}^{r}}{T^{s}}$

$- q + r = 0$ $. . . (i)$

$p - 3 q + r = - 1$ $. . . (i i)$

$4 q - 3 r - s = 0$ $. . . (i i i)$

$2 q - r = 1$ $. . . (i v)$

$Solving (i), (ii), (iii) and (iv)$

$p = 1, q = 1, r = 1, s = 1$

Solution

Q.
Consider the equation $H = \frac{x^{p} ε^{q} E^{r}}{t^{s}}$

Where $H$ = magnetising intensity; $E$ = electric field; $ε$ = permittivity, $x$ = distance, $t$ = time. The values of $p, q, r$ and $s$ respectively are [2026]

1 1, 1, 1, 1

2 -1, 1, 2, 1

3 1, -1, -2, 1

4 -1, -2, -2, 1

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