Forgive my ignorance, but I didn't know there was a master's degree route for law. Do you mean you want to get your JD and become a practicing lawyer? I know that some friends of friends from undergrad that studied chemistry and physics and are finishing law school so they could work in patent law.
If there are any science/engineering based law courses at your university you can take those. You will need to be good at learning how to write; law school will drill this into you but it would be good to have a head start if your English department has related courses. Join Toastmasters or something, you may go to court someday!
From Study.com: "The first degree students can enroll in is a Juris Doctor (J.D.) degree program, which can be completed after three years of full-time study. The second law degree is the Master of Laws (LL.M.), and the third degree is the Doctor of Juridical Science (S.J.D.)." To slightly paraphrase jari001's question: "Do you want to become a practicing lawyer or increase your legal expertise?"
Either way, you're going into a definite "niche" between engineering and law. Engineers don't talk "law" and lawyers don't talk "engineering" -- having a foot in both worlds will lead to interesting opportunities.
If you want to get into expert testimony, don't pursue law education. Pursue a masters level engineering education and valuable work experience, then build a resume of credentials tied to a specific corner of your field.
If you want to get into law, stash your engineering bachelors degree and go to law school. Engineering degrees are looked favorably upon by law programs, so you actually have a pretty good leg up on this path.
Both are rewarding paths. The low end of the law business is lower than the low end of engineering, but the top end is much, much higher when rated by $$ compensation.
If you wanted to be some kind of high powered blend of engineer and lawyer, you'll probably want to take the first path, then mid career fill in the second path. But you won't be doing expert testimony in your cases if you're the trial lawyer in the case, you'll still have to bring someone else in to fill that role. Can't interview yourself on the stand, and even if you could, it wouldn't be credible to do so.
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