Our solar system is composed of the Sun, 8 planets that orbit it, many more dwarf planets, and two asteroid belts. Just as happens in many questions in the field of sciences, the answer is more complicated than it may seem, and there is not always a unique answer.
Beyond the magnetic influence of the Sun: the heliopause
The radiation emitted by the Sun, known as the solar wind, is composed of plasma and ionised material that travels through space at a gigantic speed. This radiation disappears at approximately 17 billion kilometres from the Earth. The interior of this zone is known as the heliosphere, and, inside it, it is considered that an object is found under the Sun’s magnetic influence.
The limit where the heliosphere ends is known as the heliopause. NASA considers that the probes that cross the heliopause are found in the interstellar medium. For example, the Voyager 1 probe, the farthest way object created by humans, crossed this border in 2013, and many media affirmed that it had left the solar system.
However, this isn’t totally exact, since beyond Neptune’s orbit and the Kuiper belt (a belt formed by an enormous quantity of asteroids and comets) is found in the Oort cloud. This “cloud” is a sphere that completely surrounds the solar system, and is formed by trillions of asteroids, comets and other bodies. It spreads for about two light-years from the Sun.
The Sun’s gravitational attraction
These trillions of bodies that form the Oort cloud orbit the Sun, so they are consequently subject to its gravitational attraction. The Voyager probe will take about 300 years to arrive at the beginning of the Oort cloud, and another 30 000 years will pass until it gets entirely through it.
As we can see, these objects are still found under the influence of the Sun’s gravity, and we could consider that the Oort cloud forms part of the solar system.
Therefore, on one hand, we can affirm that the limit of the solar system is found in the heliopause, and, on the other hand, that the solar system continues to the end of the Oort cloud. It all depends on what we want to keep in mind, and, consequently, there isn’t a unique answer.