# Magnetic field of a long solenoid

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1. Nov 28, 2015

### shinobi20

1. The problem statement, all variables and given/known data
A long solenoid has current I flowing through it, also denote N as the turns per unit length. Take its axis to be the z-axis, by symmetry the only component of the magnetic field inside is Bz. Find the magnetic field at the center of the solenoid (on the axis). Also, find the magnetic field at the ends of the solenoid.

2. Relevant equations
Ampere's Law

3. The attempt at a solution
For the first part, since the solenoid is long we can approximate the magnetic field inside to be uniform and is given by BzoNI, so we can say that the magnetic field at the center is also μoNI. I'm not sure if my argument is correct but based on my understanding, from the uniformity of the B field inside, it should be the same everywhere inside. Can anyone kindly tell me if this is correct? Any suggestions and insights?

For the second part I don't have any idea on how to start.

2. Nov 28, 2015

### Staff: Mentor

Right.

For the second part, you can use symmetry: imagine you are in the middle of the solenoid, and split it in two parts: "below" and "above" (along the z axis).

3. Nov 28, 2015

### shinobi20

If you split the solenoid into two parts, then the total magnetic field inside each half solenoid would also be half as much but I can't see how I can tell the magnetic field at both ends by imagining to be in the middle. Can you expound more?

4. Nov 29, 2015

### Staff: Mentor

The middle is just the sum of two ends.