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

Step-by-step solution

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 [ ] = [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 = x^p ^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