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

The dimensional formulas for the given physical quantities are:

Magnetic field intensity \([H] = [M^0 L^{-1} T^0 A^1]\)

Distance \([x] = [M^0 L^1 T^0 A^0]\)

Permittivity \([\epsilon] = [M^{-1} L^{-3} T^4 A^2]\)

Electric field \([E] = [M^1 L^1 T^{-3} A^{-1}]\)

Time \([t] = [M^0 L^0 T^1 A^0]\)

Given the equation \(H = \dfrac{x^p \epsilon^q E^r}{t^s}\), we can write it in terms of dimensions as:

\([M^0 L^{-1} T^0 A^1] = [L]^p [M^{-1} L^{-3} T^4 A^2]^q [M L T^{-3} A^{-1}]^r [T]^{-s}\)

Combining the powers of \(M, L, T\), and \(A\) on the right side:

\([M^0 L^{-1} T^0 A^1] = [M^{-q+r} L^{p-3q+r} T^{4q-3r-s} A^{2q-r}]\)

Equating the powers of corresponding fundamental quantities from both sides:

For \(M\): \(0 = -q + r \implies q = r\)

For \(A\): \(1 = 2q - r\)

Substituting \(r = q\) into the equation for \(A\):

\(1 = 2q - q \implies q = 1\)

Since \(q = r\), we get \(r = 1\).

For \(L\): \(-1 = p - 3q + r\)

Substituting \(q = 1\) and \(r = 1\):

\(-1 = p - 3(1) + 1 \implies -1 = p - 2 \implies p = 1\)

For \(T\): \(0 = 4q - 3r - s\)

Substituting \(q = 1\) and \(r = 1\):

\(0 = 4(1) - 3(1) - s \implies 0 = 1 - s \implies s = 1\)

Thus, the values are \(p = 1\), \(q = 1\), \(r = 1\), and \(s = 1\).

Answer: \(1, 1, 1, 1\)