  The merger of two magnetized compact objects, such as neutron stars, forms a
compact object which may launch a relativistic and collimated jet. Numerical
simulations of the process show that a dense and highly magnetized medium
surrounds the system. This study presents a semi-analytical model that models
the effects that a static magnetized medium with a tangled field produces in
relativistic, collimated, and non-magnetized jets. The model is a first
approximation that addresses the magnetic field present in the medium and is
based on pressure equilibrium principles between the jet, cocoon, and external
medium. A fraction of the ambient medium field is allowed to be entrained in
the cocoon. We find that the jet and cocoon properties may be affected by high
magnetic fields ($\gtrsim 10^{15}$~G) and mixing. The evolution of the system
may vary up to $\sim10\%$ (compared to the non-magnetized case). Low-mixing may
produce a slower-broader jet with a broader and more energetic cocoon would be
produced. On the other hand, high-mixing could produce a faster-narrower jet
with a narrow and less-energetic cocoon. Two-dimensional hydrodynamical
simulations are used to validate the model and to constrain the mixing
parameter. Although the magnetic field and mixing have a limited effect, our
semi-analytic model captures the general trend consistent with numerical
results. For high magnetization, the results were found to be more consistent
with the low mixing case in our semi-analytic model.
