Consider the equation $H=\frac{x^{p} \epsilon^{q} E^{r}}{t^{s}}$ Where $\mathrm{H}=$ magnetic field; $\mathrm{E}=$ electric field; $\epsilon=$ permittivity, $\mathrm{x}=$ distance, $\mathrm{t}=$ time. The values of $p, q, r$ and $s$ respectively are :

JEE Main · 2026 · 08 Apr 2026 · Shift 2 · Units & Measurement

Consider the equation

H = \frac{x ^{p} ϵ ^{q} E ^{r}}{t ^{s}}

Where

H =

magnetic field;

E =

electric field;

ϵ =

permittivity,

x =

distance,

t =

time. The values of

p, q, r

and

s

respectively are :

Answer: (A)

Taking

H

as the magnetic field intensity,

[H] = I L^{- 1}

, with

[E] = M L I^{- 1} T^{- 3}

[ϵ] = M^{- 1} L^{- 3} I^{2} T^{4}

[x] = L

and

[t] = T

. Substituting into

H = \frac{x ^{p} ϵ ^{q} E ^{r}}{t ^{s}}

and balancing each dimension: mass gives

- q + r = 0

, current gives

2 q - r = 1

, length gives

p - 3 q + r = - 1

, and time gives

4 q - 3 r - s = 0

. Solving these,

q = 1

r = 1

p = 1

and

s = 1

. The values of

p, q, r, s

are

1, 1, 1, 1

JEE Main · 2026 · 08 Apr 2026 · Shift 2 · Single correct option