A parallel plate capacitor with circular plates of radius R is being charged by a constant current. Let B₁ be the magnitude of the induced magnetic field in the region between the plates at a radial distance r = R 2 from the central axis, and B₂ be the magnitude of the magnetic field at a radial distance r = 2R from the central axis. The ratio B₁ B₂ is :

Step-by-step solution

Using the Ampere-Maxwell law, the line integral of the magnetic field is given by B d l = ₀ I_ enc , where I_ enc is the enclosed displacement current. The total displacement current between the plates is equal to the charging current I . The displacement current density is uniform and given by J_d = I R^2 . For a point inside the region between the plates ( r I_ enc = J_d ( r^2) = I r^2 R^2 Applying the Ampere-Maxwell law: B(2 r) = ₀ I r^2 R^2 B = ₀ I r 2 R^2 At r = R 2 , the magnetic field B₁ is: B₁ = ₀ I ( R 2 )