how to pass a null value to a foreign key field?

I have 2 tables:

university:

university_id(p.k) | university_name

and user:

uid | name | university_id(f.k)

How to keep university_id NULL in user table?

I am writting only 1 query, my query is:

INSERT INTO user (name, university_id) VALUES ($name, $university_id);

Here $university_id can be null from front end.

university table will be set bydefault by me.

In the front end, student will select the university name, according to that the university_id will pass to user table, but if student is not selecting any university name then is should pass null value to the user table for university_id field.