Q. Consider the equation: H=xpϵqErtsH = \frac{x^p \epsilon^q E^r}{t^s}H=tsxpϵqEr Where: H = magnetic field E = electric field ε = permittivity x = distance t = time Find the values of p, q, r and s respectively.
Consider the equation H = (x p ε q E r ) / t s Where: H = magnetic field, E = electric field, ε = permittivity, x = distance, t = time Find the values of p, q, r and s. Step 1: Dimensions of Each Quantity Quantity Dimensions H (Magnetic field) [M T⁻² A⁻¹] E (Electric field) [M L T⁻³ A⁻¹] ε (Permittivity) [M⁻¹ L⁻³ T⁴ A²] x (Distance) [L] t (Time) [T] Step 2: Dimensional Equation Substituting dimensions into the equation: [M T⁻² A⁻¹] = [L]ᵖ × [M⁻¹L⁻³T⁴A²]ᶠ × [MLT⁻³A⁻¹]ʳ × [T]⁻ˢ Expanding: [M 1 T -2 A -1 ] = [M -q+r L p-3q+r T 4q-3r-s A 2q-r ] Step 3: Compare Powers on Both Sides Element Equation Result M -q + r = 1 Equation (1) ...