The problem states:
Inside a right circular cylinder, ,- 800μ while the exterior is free space. Given that B, -,(22a, +45a,) Wb/m2, determine B, just outside the cylinder.
Since the inside of the cylinder has permittivity ,- 800μ and the outside is free space with ,0 = 8.85*10^-12 F/m, by Ampere's Law and Gauss's Law we know that:
B inside cylinder = (22a, +45a,) Wb/m2
B outside cylinder = k*B inside cylinder
Where k = ,0 / ,- = 8.85*10^-12 / 800*10^-6 = 0.011
Therefore,
B just outside the cylinder = (0.011)*(22a, +45a,)
= (22a, +45a,) * 0.242 Wb/m2
So the answer is:
B just outside the cylinder = (22a, +45a,) * 0.242 Wb/m2