It might help if you said more about what you have in mind. The real magnetic pole, such as it is, isome thoudands of km underground, so no bomb that we exploded  would be likely to make much difference to it. The field in turn is so weak that it would have very little influence on the charged particles that the bomb created or released. Even if the pole did stick out, the bomb could have very little effect.

And if somehow it did destroy the Earth's magnetic field, I reckon it would have very little effect on the planet, apart from some ecological effects and some nuisance effects for people with a need to use magnetic compasses.