# [Physics] Magnetic field of a solenoid vs a circular loop

applied-physicselectromagnetism

Why doesnt the magnetic field inside a solenoid depend on its radius whereas the magnetic field inside a circular loop or a coil depends on its radius?Please explain using simple language keeping in mind that I'm a 10th standard student.

Circular loop

As you stated, the magnetic field inside a circular loop depends as the inverse of it's square radius. This a direct result from the calculation of the magnetic field, which can be obtained using the Biot-Savart formula. Don't worry if you haven't studied it yet, because what is important is that the bigger the circular coil, the smaller the magnetic field becomes for a given current. This can be better visualized with the following image from Hyperphysics:

Solenoid

You've been taught that the magnetic field of a solenoid, on the other hand, doesn't depend on its radius. However, this is just an idealization that applies for a perfect solenoid, that is, a solenoid which has a small radius and is infinitely long. This allows one to consider all the lines of the magnetic field as parallel all along the inside of the solenoid, which traduces in the magnetic field being constant everywheres inside the solenoid. This image from Quora will help you visualize it:

I think the best analogy for the magnetic field in a solenoid would be a tube (with a constant diameter) through which water flows in it. If the flux is perfect, you will measure the same velocity of water no matter where you put yourself inside the tube. In this case, the tube is your solenoid, and the velocity of water corresponds to the magnetic field.

However, in real life solenoid the magnetic field does indeed vary with the radius of the solenoid, and you could measure certain variations if you deviate from the axis of symmetry of the solenoid, like this image taken from Wikipedia:

Each blue line you see represents the value and direction of the magnetic field inside and outside of the solenoid. Since here the diameter of the solenoid is bigger than its length, you can see that as we approach the border the magnetic field does change. Therefore, the best solenoids are those who have a small diameter in comparison with their length.