Magnitude of magnetic flux of a solenoid using Biot-Savart law

[MorrowUoN]

Homework Statement

A 10 cm long, 1 cm diameter solenoid contains 500 turns of wire. A current that varies as I = 5Sin(100πt) Amps flows through the solenoid wire. Calculate the magnitude of the magnetic flux at the centre of the solenoid as a function of time using equation (1). Compare this with the value for an infinitely long solenoid.

Homework Equations

B = ((μ₀*I*n)/2)(sin∅₂-sin∅₁) (1)

The Attempt at a Solution

Having trouble attempting since this is lab homework and we are yet to cover this material in lectures. Also, sorry if this isn't considered advanced physics by this forums standards however, this is a first year 'Advanced Physics' class.

 

[gabbagabbahey]

Homework Statement

A 10 cm long, 1 cm diameter solenoid contains 500 turns of wire. A current that varies as I = 5Sin(100πt) Amps flows through the solenoid wire. Calculate the magnitude of the magnetic flux at the centre of the solenoid as a function of time using equation (1). Compare this with the value for an infinitely long solenoid.

Homework Equations

B = ((μ₀*I*n)/2)(sin∅₂-sin∅₁) (1)

The Attempt at a Solution

Having trouble attempting since this is lab homework and we are yet to cover this material in lectures. Also, sorry if this isn't considered advanced physics by this forums standards however, this is a first year 'Advanced Physics' class.

Hi MorrowUoN, welcome to PF!

I suggest you start by drawing a picture (almost always a good idea when you are stuck)... what are ∅₁ and ∅₂ when your field point (the point you are calculating the magnetic flux at) is at the centre of the solenoid?

 

[MorrowUoN]

The notes have this formula for calculating the sin and cos term however, I am not sure which details are x, R and l from the question. I guess it doesn't hurt to hazard a guess, would l be the length, R the radius (with diameter given in this case) and x be the distance of point P from the centre, making x = 0 in this case?

Thanks for your reply :)

 

[gabbagabbahey]

The notes have this formula for calculating the sin and cos term however, I am not sure which details are x, R and l from the question. I guess it doesn't hurt to hazard a guess, would l be the length, R the radius (with diameter given in this case) and x be the distance of point P from the centre, making x = 0 in this case?

Thanks for your reply :)

Seems like a reasonable guess to me, but math and physics is not really about guessing . To be sure, I again recommend that you draw a picture and label the relevant distances and angles. A little bit of trigonometry will give you your answer.

 

[Nickie]

As a scientist, it is important to understand the fundamental principles and laws that govern our physical world. In this case, we are dealing with the Biot-Savart law, which describes the magnetic field produced by a current-carrying wire. This law is crucial in understanding the behavior of solenoids and other electromagnets.

To begin with, we have been given a solenoid with specific dimensions and a varying current. Using equation (1), we can calculate the magnitude of the magnetic flux at the center of the solenoid as a function of time. This equation takes into account the factors of current, number of turns, and the permeability of free space (μ0).

However, it is important to note that equation (1) assumes an ideal solenoid with infinite length. In reality, the length of the solenoid is finite and this can affect the magnitude of the magnetic flux. As the length of the solenoid increases, the magnetic field becomes more uniform and the flux increases. Therefore, the value obtained from equation (1) may differ from the actual value for a solenoid with finite length.

In order to compare the value obtained from equation (1) with that of an infinitely long solenoid, we can use the concept of self-inductance. This is a property of a solenoid that describes its ability to produce a magnetic field in response to a changing current. An infinitely long solenoid has a higher self-inductance compared to a solenoid with finite length, resulting in a larger magnitude of magnetic flux.

In conclusion, as a scientist, it is important to understand the limitations and assumptions of equations and laws, and to consider real-world factors when analyzing physical systems. While equation (1) can provide an estimate of the magnitude of magnetic flux for a solenoid with finite length, it is important to keep in mind that the actual value may differ.