# Magnetic field of a solenoid vs a circular loop

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.

• So that means it's just an assumption and B inside a solenoid actually depends on its radius as well. Commented Oct 4, 2018 at 15:50
• Yes, it's actually an approximation that works well with practical applications. But if you want to be precise, it does vary with the radius. I just found a simple derivation here (view graph 9): spiff.rit.edu/classes/phys313/lectures/sol/sol_f01_long.html Commented Oct 4, 2018 at 15:57
• You can see when they make $D=0$ the magnetic field expression reduces to the one you're probably familiar with (it doesn't depend on the radius). The idealization for a perfect infinite solenoid is just basically saying that the magnetic field in the axis of the solenoid is the same away from it, as long as you're inside the solenoid and far away from its borders. Commented Oct 4, 2018 at 15:59