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.