How Much Current Is Needed for a Solenoid to Generate a Specific Magnetic Field?

[jena]

Hi,

My Question:

A 50.0-cm long solenoid 1.25cm in diameter is to produce a field of 0.385 T at its center. How much current should the solenoid carry if it has 975 turns of the wire?

I know that I have to use this equation:

B = \mu _0 nI


where I'm stuck at is with the length do I used the how long it is with the diameter or do i just ignore the diameter

please help

Thank You

 

[mukundpa]

1
The formula you have written is for a long solenoid such that L >>R, to insure this, I think the dimeter is given, otherwise you have to use general formula for the field.
2
In this formula 'n' is the number of turns per unit length n = N/L.

 

[quicknote]

Hello,

Thank you for your question. In this situation, you can ignore the diameter of the solenoid and just use the length of 50.0 cm. The diameter does not affect the calculation for the current in a solenoid.

To find the current, you can rearrange the equation B = \mu _0 nI to solve for I. It would look like this:

I = B/(\mu _0 n)

Now, substitute the given values into the equation:

I = (0.385 T) / (4\pi x 10^{-7} Tm/A) x (975 turns)

Simplifying, you get:

I = 0.385 T / 3.85 x 10^{-4} A

I = 1000 A

Therefore, the solenoid should carry a current of 1000 A to produce a field of 0.385 T at its center.

I hope this helps! Let me know if you have any other questions.

Best,