I am trying to determine the external magnetic field of a solenoid at a given distance from its z-axis. Currently, I have been able to find the biot savart law for a current loop:

How would I determine the external magnetic field strength of a solenoid from this equation  ?

Since each turn on a solenoid can be considered as one current loop, I presume there is a way to "add up" magnetic field strengths of a solenoid with n number of turns (current loops). We can also roughly equate the z squared + R squared , all to the power of 3/2, as just z cubed , when z is significantly bigger than R.

I think integrating the formula would give the answer, but since I am only familiar with very basic calculus ( i.e. basic definite integrals), I am not sure how to go about this. If anyone uses calculus, please be so kind to add the steps for my own understanding (no matter how simple !)

(Note,I only started 10th grade this fall, so please take this into account into your answers !)

I am trying to determine the external magnetic field of a solenoid at a given distance from its $z$-axis. Currently, I have been able to find the Biot-Savart law for a current loop: $$B_{z}=\frac{\mu_{0}}{4\pi}\frac{2\pi R^{2}I}{(z^{2}+R^{2})^{3/2}}.$$ How would I determine the external magnetic field strength of a solenoid from this equation?

Since each turn on a solenoid can be considered as one current loop, I presume there is a way to "add up" magnetic field strengths of a solenoid with $n$ number of turns (current loops). We can also roughly equate the $(z^{2}+R^{2})^{3/2}$ as just $z^{3}$ , when $z$ is significantly bigger than $R$.

I think integrating the formula would give the answer, but since I am only familiar with very basic calculus (i.e. basic definite integrals), I am not sure how to go about this. If anyone uses calculus, please be so kind to add the steps for my own understanding (no matter how simple !)

(Note, I only started 10th grade this fall, so please take this into account into your answers !)

I am trying to determine the external magnetic field of a soleneoid at a given distance from its z-axis. Currently, I have been able to find the biot savart law for a current loop:

How would I determine the external magnetic field strength of a solenoid from this equation ?

Since each turn on a solenoid can be considered as one current loop, I presume there is a way to "add up" magnetic field strengths of a solenoid with n number of turns (current loops). We can also roughly equate the z squared + R squared , all to the power of 3/2, as just z cubed , when z is significantly bigger than R.

I think integrating the formula would give the answer, but since I am only familiar with very basic calculus ( i.e. basic definite integrals), I am not sure how to go about this. If anyone uses calculus, please be so kind to add the steps for my own understanding (no matter how simple !)

(Note,I only started 10th grade this fall, so please take this into account into your answers !)

I am trying to determine the external magnetic field of a solenoid at a given distance from its z-axis. Currently, I have been able to find the biot savart law for a current loop:

How would I determine the external magnetic field strength of a solenoid from this equation ?

Since each turn on a solenoid can be considered as one current loop, I presume there is a way to "add up" magnetic field strengths of a solenoid with n number of turns (current loops). We can also roughly equate the z squared + R squared , all to the power of 3/2, as just z cubed , when z is significantly bigger than R.

I think integrating the formula would give the answer, but since I am only familiar with very basic calculus ( i.e. basic definite integrals), I am not sure how to go about this. If anyone uses calculus, please be so kind to add the steps for my own understanding (no matter how simple !)

(Note,I only started 10th grade this fall, so please take this into account into your answers !)