- #1
Bryon
- 99
- 0
Homework Statement
A solenoid has length L = 20 cm, radius 6 cm, and N1 = 4500 turns; its axis coincides with the z-axis. A circular conducting loop containing N2 = 11 turns of radius a = 1 cm is centered inside the solenoid; the plane of the loop makes a 30° angle with respect to the z-axis.
The current in the windings of the solenoid is varying with time according to the expression
I1(t) = 0.45 A + 0.14 (A/s) t.
Homework Equations
Biot-Savart(Center of a solenoid): Bz = u0nI
Magnetic flux: ϕ = ∫BdA= NBAcosϑ
The Attempt at a Solution
(a) Calculate the magnitude of the magnetic flux Φm through the loop at t = 3 s. (Absolute value)
I1(3s) = 0.45 A + 0.14 (A/s) (3s) = 0.87A
Bz = 4*pi*10^(-7)*(4500/0.2)*0.87 = 0.02459867 T
ϕ = (0.02459867 )*pi*(.01^2)*11*cos(30) = 7.3618137e-5 Tm^2
I did something wrong and I am not quite sure where. Any ideas?
I think i understand the concept. Since there is a small loop inside the solenoid at angle ϑ, I need to find the magnetic field at the center due to the current in the solenoid. Then I just have to find the total flux through the total area of the small circular loop that is sitting in the middle of the solenoid.
The question does provide a hint: Approximate this finite solenoid by an equivalent infinite solenoid to find the magnetic field in the central region.
Does this mean I can use a portion of the number of turns over a small distance to find the magnetic field?
Last edited: