Magnetic Field involving solenoids

In summary, when two long ideal solenoids with radii of 20 mm and 30 mm respectively, carrying the same number of turns of wire per unit length, are mounted inside each other along a common axis, the magnetic field within the inner solenoid will be zero. This indicates that the current in the inner solenoid must be equal to the current in the outer solenoid, making the correct answer E. The formula for the magnetic field inside a current-carrying solenoid is B = μ_o * i * n, where n is the number of turns of wire per unit length.
  • #1
McAfee
96
1

Homework Statement



Two long ideal solenoids (with radii 20 mm and 30 mm respectively) carry the same number of turnes of wire per unit length. The smaller solenoid is mounted inside the larger, along a common axis. It is observed that the magnetic field within the inner solenoid is zero. The current in the inner solenoid must be:

A. two-thirds the current in the outer solenoid
B. one-third the current in the outer solenoid
C. twice the current in the outer solenoid
D. half the current in the outer solenoid
E. the same as the current in the outer solenoid

This one is hard. If you could please provide an explanation with the answer so I could better understand this.
THanks in advance.

Homework Equations



n/a

The Attempt at a Solution



Right now I'm ruling out answer A.
 
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  • #2
Hi McAfee! :smile:
McAfee said:
Two long ideal solenoids (with radii 20 mm and 30 mm respectively) carry the same number of turnes of wire per unit length. The smaller solenoid is mounted inside the larger, along a common axis. It is observed that the magnetic field within the inner solenoid is zero.

Call the currents I and J.

Hint: what is the formula for the magnetic field inside a current-carrying solenoid?

And can we just add the fields?
 
  • #3
tiny-tim said:
Hi McAfee! :smile:Call the currents I and J.

Hint: what is the formula for the magnetic field inside a current-carrying solenoid?

And can we just add the fields?

The formula is B = μ_o*i*n

n is the number of turns
and yes
 
  • #4
yup! :smile:

so what's the total equation, and is it A B C D or E ? :wink:
 
  • #5
20mm = .02
30mm = .03

assuming that I can ignore n because it will be the same for both.
Would it be E because the radii doesn't play a role in the equation?
 
  • #6
sorry, i missed your post :redface:
McAfee said:
assuming that I can ignore n because it will be the same for both.
Would it be E because the radii doesn't play a role in the equation?

yes the radii don't matter,

so if (case E) the currents are equal (and opposite), then the magnetic field inside the inner solenoid will be zero :smile:
 

1. What is a solenoid?

A solenoid is a coil of wire that produces a magnetic field when an electric current is passed through it. It is typically made up of many loops of wire wrapped around a cylindrical core.

2. How is a solenoid's magnetic field created?

When an electric current flows through the wire of a solenoid, it creates a magnetic field because the moving electrons in the wire create a circular magnetic field around the wire. The magnetic field is strengthened by the multiple loops of wire in the solenoid.

3. What factors affect the strength of a solenoid's magnetic field?

The strength of a solenoid's magnetic field is affected by the number of loops in the coil, the amount of current flowing through the wire, and the material of the core. Increasing any of these factors will increase the strength of the magnetic field.

4. How is the direction of a solenoid's magnetic field determined?

The direction of a solenoid's magnetic field can be determined using the right-hand rule. If you point your thumb in the direction of the current flow, your fingers will curl in the direction of the magnetic field lines.

5. What are some real-world applications of solenoids and their magnetic fields?

Solenoids are used in a variety of everyday devices, such as doorbells, speakers, and electric motors. They are also used in industrial applications for things like controlling valves and switches, and in medical devices like MRI machines. In addition, solenoids are used in research and scientific experiments to create and control magnetic fields.

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