# Need Help with double solenoid magnetic field question

## Homework Statement

There are two coaxial solenoids, each 30cm long. One is inside the other. Each carry a current of 3A, but in opposite directions. Inner solenoid has a radius of 3cm and the outer has a radius of 6cm. Inner has 15 turns/cm and the outer has 30 turns/cm. Find the magnitude and direction of the magnetic field inside the solenoid, between the inner and outer solenoids, outside the outer most solenoid. What is the inductance of the inner solenoid? The outer?

B=(uNI)/l

## The Attempt at a Solution

B due to the outer solenoid turns out to be 360piX10^-5 T and for the inner it is 180piX10^-5 T So for the magnetic field in the inner solenoid it would be the difference between the two fields since they are going in the opposite direction. THis makes it 180piX10^-5 T in the direction that the outer solenoid dictates. How do I get the field between them and outside the oter most solenoid? Thanks.

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Also, would the current running in opposite directions affect the inductance?

tiny-tim
Homework Helper
Welcome to PF!

Hi Turpulus! Welcome to PF!
… How do I get the field between them and outside the oter most solenoid?
We usually assume that, if a solenoid is long enough, the magnetic field it creates outside it is zero.

Ok that definitely helps. Is 30cm long enough though? Also, would the inductance be affected by the solenoids nested inside each other or is that an intrinsic property of each solenoid?

tiny-tim
Homework Helper
Ok that definitely helps. Is 30cm long enough though?
For exam questions? yes

In reality? no idea
Also, would the inductance be affected by the solenoids nested inside each other or is that an intrinsic property of each solenoid?
The magnetic fields are independent.

For exam questions? yes

In reality? no idea

The magnetic fields are independent.
So if the magnetic fields are independent, then that means the inductances are independent also correct? Won't the magnetic fields be cumulative in the inner solenoid?

tiny-tim
Homework Helper
Independent means cumulative!

Independent means cumulative!

Ok great. I think I'm getting it. Would I subtract the inductances from one another instead of add them since the current is flowing in opposite directions? For the individual solenoids, I calculated an inductance of 2.398mH for the inner and 38.373 for the outer. So the outer inductance would remain 38.373mH, but the inductance of the inner would actually be 38.373mH - 2.398mH? I'm using L=((uN^2)A)/length of solenoid to calculate the individual inductances. Just not sure how to add or subtract them. Thanks again!

tiny-tim
Homework Helper
looking back, i'm a little confused …

the question doesn't ask for a total inductance

and are they wired in parallel or in series (or not electrically connected at all?)