# What is Iencl, the current passing through the chosen loop?

Part D. What is Iencl, the current passing through the chosen loop?

Express your answer in terms of L (the length of the Ampèrean loop along the axis of the solenoid) and other variables given in the introduction.

Part E. Find Bin, the z component of the magnetic field inside the solenoid where Ampère's law applies.

Express your answer in terms of L, D, n, I, and physical constants such as ?0.

D). The magnetic field of a solenoid by considering a rectangular path is,

\oint B \cdot d s =\oint B \cdot d s+\oint B \cdot d s+\oint B \cdot d s+\oint B \cdot d s

=0+0+B l+0

=B L

Zero value comes when the angle between the magnetic field line and the area is perpendicular to each other which results in \cos 90^{\circ}. As the flux is the equal to the dot product of magnetic field and the area enclosed.

Use Ampere's Circuital law.
B l =\mu_{0} N I

B =\frac{\mu_{0} N I}{L}

=\mu_{0} n I

Here, n=\frac{N}{L}

The ampere's law is,

\oint B \cdot d s=\mu_{0} I_{\mathrm{mc}}

B L =\mu_{0} I_{\mathrm{mc}}

I_{\mathrm{enc}} =\frac{B L}{\mu_{0}}

Substitute the value of B.

I_{\mathrm{enc}}=\frac{\left(\mu_{0} n I\right) L}{\mu_{0}}

I_{\mathrm{mc}}=n \pi

E). The ampere's law is,

\oint B \cdot d s =\mu_{0} I_{\mathrm{enc}}

B L =\mu_{0}(n I L)

B =\frac{\mu_{0} n I Z}{L^{\prime}}

B =\mu_{0} n I

### Raymond Puzio

Raymond Puzio has a PhD in Physics from Yale University. I have been creating PlanetPhysics with Aaron Krowne and Ben Loftin since 2005.