When an ball made of uniform magnetic is introduced into an external unifrom magnetic induction `B` inside the ball with permeability `mu`, recall that the magnetic field is inside a unifromly mag netized ball is unifrom and its strength is equal to `H' = J//3`, where `J` is the magnetization.

Explanation

We use the that the within an isoloted uniformly manetized ball,
`vec(H') = vec(J)//3, vec(B) = (2 mu_(0) vec(J))/(3)`, where `vec(J)` is the magnetization vector, Then in a unifrom magnetic fiedl with induction `vec(B_(0))`, we have superpostion,
`vec(B)_(i n) = vec(B)_(0) + (2 mu vec(J))/(3), vec(H)_(i n) = (vec(B)_(0))/(mu_(0)) -vec(J)//3`
or, `vec(B)_(i n) + 2mu_(0) vec(H)_(i n) = 3 vec(B)_(0)`
also, `vec(B)_(i n) = mu mu_(0) vec(H)_(i n)`
Thus, `vec(H)_(i n) = (3 vec(B)_(0))/(mu_(0) (mu + 2))` and `vec(B)_(i n) = (3 mu vec(B)_(0))/(mu + 2)`