# Explanation of the wording - Electromagnetism Question

Could someone explain the wording (and possibly see if I'm going the right way about it) of this question to me.

What is the current required in the windings of a long solenoid that has 1000 turns uniformly distributed over a length of 0.400m, o produce at the centre of the solenoid a magnetic field of magnitude 0.1mT.

The wording I'm concerned about is about the turns. Is the wire 40cm long with 1000 turns, or is each turn 40cm long?

Anyway to the working:

I thought initially to use F=nBIl, but as no force is given I can't use it can I? Is it something to with Biot-Savart's law?

I want to use the form, B= NI(mew0)/2a, but I can't think how to find a, the distance to the center of the circular loop. Any hints?

## Answers and Replies

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Hootenanny
Staff Emeritus
Gold Member
I would say that the total length of the wire is 40cm long. The fact that it says the turns are uninformally distrobuted over 40cm kinda gives it away

I'd go with that. I think I have it sussed from here. (Actually I reread the question and it made sense!)

D'oh!

Andrew Mason
Homework Helper
Brewer said:
Could someone explain the wording (and possibly see if I'm going the right way about it) of this question to me.

What is the current required in the windings of a long solenoid that has 1000 turns uniformly distributed over a length of 0.400m, o produce at the centre of the solenoid a magnetic field of magnitude 0.1mT.

The wording I'm concerned about is about the turns. Is the wire 40cm long with 1000 turns, or is each turn 40cm long?
It means the solenoid length is .4 m. You don't care about the length of the wire.

I thought initially to use F=nBIl, but as no force is given I can't use it can I? Is it something to with Biot-Savart's law?

I want to use the form, B= NI(mew0)/2a, but I can't think how to find a, the distance to the center of the circular loop. Any hints?
The magnetic field at the centre of a long solenoid (ie. all lines of force go through the centre) is given by Ampere's law for a rectangular path through the centre and enclosing all the windings: $\oint B\cdot ds = \mu I$. Since B is constant throughout the solenoid length and the rest of the path integral sums to 0, the left side works out to BL. Work out the right side (keeping in mind that I is the current enclosed by the path) and that will enable you to find the expression for I in terms of B, L and N.

AM