Two Solenoids on top of each other?

[MyAmpsGoTo11]

Homework Statement

A 121-turn solenoid with a length of 27 cm and radius of 0.6 cm carries a current of 1.1 A. A second coil of 4 turns is wrapped tightly about this solenoid so that it can be considered to have the same radius as the solenoid. Find the change in the magnetic flux through the coil when the current in the solenoid increases to 4.2 A in a period of 1.13 s. The permeability of a vacuum is 4 pi × 10^-7 T • m/A Answer in units of T • m².

Homework Equations

Magnetic flux = permeability of a vacuum X N² X A X I / length

The Attempt at a Solution

Change in magnetic flux = permeability of a vacuum X 125² X A X 4.2 / length - permeability of a vacuum X 125² X A X 1.1 / length

I'm confused how many turns this would have. Would it just be 125 turns? I have no idea how to count the inductance of two solenoids together.

 

[jdc15]

If the second coil is attached to the first coil such that it carries current as well, then yes, you would treat it as a 125 coil single solenoid. However, if it doesn't carry current, then it's presence is negligible, since it has negligible mass and volume. Thus you would again use 121 coils.

 

[inutard]

I believe you would use four turns, as the flux is induced in the four turn coil by the 121 turn coil. You will need to know that:
Change in Flux = Change in Field * Cross sectional Area
Change in field = permeability of a vacuum x N x A x (I/t) / length
**Note that it is N and not N^2 as you have previously specified.

 

[jdc15]

Ah right, misinterpreted the question a bit. First use 121 coils to determine the induced magnetic field, then use 4 coils when finding the change in flux.

 

[inutard]

Precisely. Good luck on the rest of the question.