# Magnetic field inside a Solenoid

• Prashasti
In summary, the magnetic field inside a solenoid can be calculated using the Biot-Savart law if the solenoid is closed.
Prashasti

## Homework Statement

Can I derive an equation for magnetic field inside a solenoid using the formula for magnetic field on the axis of a current carrying coil?

## Homework Equations

B = μI/2r ( Magnetic field at the centre of a current carrying coil)

## The Attempt at a Solution

B = μI/2r
Let the number of turns per unit length of the solenoid be 'n' and its length be 'a'
So,
B = μnaI/2r
Which is definitely not equal to μnI (Calculated using Ampere's Circuital Law)
What's wrong?[/B]

Prashasti said:

## Homework Statement

Can I derive an equation for magnetic field inside a solenoid using the formula for magnetic field on the axis of a current carrying coil?

## Homework Equations

B = μI/2r ( Magnetic field at the centre of a current carrying coil)
The formula refers to the magnetic field of an infinitely long straight current-carrying wire, at distance r from the wire. It is not valid in the centre of a loop.

Plus, the formula for the mag field around an infinite, current-carrying wire is B = μI/2πr, not what you wrote.

Well, my teacher has been using that formula...

The application of the Biot Savart Law on the centerline of a current loop involves integrating the z-component.

The symmetry is such that all the terms in this element are constant except the distance element dL , which when integrated just gives the circumference of the circle. The magnetic field is then

So, if we apply the same,
z = 0 (At the centre of the loop)
So, B = μI/2R
Isn't it correct??

It is correct for the magnetic field at the centre of a single loop. If you have a coil, all loops have their magnetic field inside the other loops. You should use the formula for B(z) and sum (integrate) the contributions of all loops.

Prashasti said:
Isn't it correct??
Yes, but tha's for a single loop, using Biot-Savart. Not the thing for here..

Rather than integrate per post #5 my hint is to form a closed loop going thru the entire solenoid middle and closing outside the solenoid. You can now apply Ampere's law to get B.
Hint: contributions to the integral outside the loop may be ignored.

Prashasti

## 1. What is a solenoid?

A solenoid is a coil of wire that is tightly wound in a helical shape. It is designed to create a magnetic field when an electric current passes through it.

## 2. How does a solenoid create a magnetic field?

When an electric current flows through a solenoid, it creates a magnetic field around the coil. This is due to the interaction between the moving charges in the wire and the magnetic field they create.

## 3. Why is the magnetic field inside a solenoid considered uniform?

The magnetic field inside a solenoid is considered uniform because the closely packed coils of wire create a consistent and evenly distributed magnetic field along the axis of the solenoid.

## 4. How does the strength of the magnetic field inside a solenoid depend on the current and number of turns?

The strength of the magnetic field inside a solenoid is directly proportional to the current passing through the wire and the number of turns in the coil. Increasing either the current or the number of turns will result in a stronger magnetic field.

## 5. Can the direction of the magnetic field inside a solenoid be reversed?

Yes, the direction of the magnetic field inside a solenoid can be reversed by changing the direction of the current passing through the wire. This will cause the magnetic field lines to reverse their direction, resulting in a reversal of the overall magnetic field inside the solenoid.

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