Answer:
Please refer to the explanation below.
Explanation:
Let
Radius of parallel plate capacitor = r
Distance between parallel plates of the capacitor = R
Area of parallel plate capacitor = Ar
Area of Distance between parallel plates of the capacitor = AR
Constant Current = I₀
Permeability of free space = μ₀
Induced magnetic field = B
From the Ampere's Maxwell law the magnetic field is given by
∫B.ds = μ₀I₀
∫B.ds = μ₀I₀Ar/AR
When the radius of the plates is much less than the distance between the parallel plates (r < R)
∫B.ds = μ₀I₀πr²/πR²
∫B.ds = μ₀I₀r²/R²
s = 2πr
B.2πr = μ₀I₀r²/R²
B = μ₀I₀r²/2πrR²
B = μ₀I₀r/2πR²
When the radius of the plates is much larger than the distance between the parallel plates (r > R)
∫B.ds = μ₀I₀
B.2πr = μ₀I₀
B = μ₀I₀/2πr
Bonus:
The magnetic field will be maximum when the radius of the parallel plate capacitor is equal to he distance between the parallel plate capacitor that is r = R
B = μ₀I₀/2πR