Magnetic field penetration in a plate the penetration equation may be written as ?²?²B?= B,?where ? is the penetration depth.?

(a) Show that B(x) inside a super conducting plate perpendicular to the x?axis and of thickness ? is given by where Ba, is the field outside the plate and parallel to it; here x = 0 is at the center of the plate.?

(b) The effective magnetization M(x) in the plate is defined by B(x) ? B_a, = 4?M(x). Show that, in CGS, 4?M(x) = ? B_a, (1/8?²) (?² ? 4x²), for ? 0.

B(x)= B cosh (x/A) cosh (8/2A)