A solenoid has 850 turns of wire, a length l=33cm, and a circular cross-section
ID: 2300522 • Letter: A
Question
A solenoid has 850 turns of wire, a length l=33cm, and a circular cross-section of radius r=4.0cm. The solenoid carries a current of 2.5A in its coils. (Assume l>>r like an "ideal" solenoid)
A. Given the direction of the magnetic field shown above, indicate the direction of the current flowing in the wires. (Fill in the wires with conventional "into page" or "out of page" symbols. You need only fill the first few loops of wire.
B. What is the strenght of the magnetic field inside the solenoid? Show your work.
An electron is launched into the solenoid with an initial velocity of 9.0x10^6 m/s from the left side (Starts left going Right) of the solenoid, at an angle of 60.0 degrees to the axis of the solenoid from the left side of the sol
C. Find the components of the electron's initial velocity that are perpendicular to and parallel to the mangetic field. Show your work.
D. After the electron enters the region of uniform magnetic field, what is the radius of its helical path, as seen when looking into the left end of the solenoid? Show your work. Does the electron appear to circulate clockwise or counter-clockwise?
Bonus: Find the time required for the electron to travel the full lengh of the solenoid. Show your work
Bonus: Find the number of cycles the electron executes as it travels from one end of the solenoid to the other.
Explanation / Answer
A) figure needed to finfd the direction
B)
MAGNETIC FILED INSIDE A SOLENOID,
B = mue*N*I/L
= 4*pi*10^-7*850*2.5/0.33
= 8.092*10^-3 t
C)
Voy(perpendicular) = vo*sin(60) = 9*10^9*sin(60) = 7.794*10^6 m/s
Vox(paralle) = vo*cos(60) = 9*10^9*cos(60) = 4.5*10^6 m/s
D)
q*voy*B = m*voy^2/r
==> r = m*voy/(B*q)
= 9.1*10^-31*7.794*10^6/(8.092*10^-3*1.6*10^-19)
= 5.478*10^-3 m
= 5.478 mm
E) figure needed to find the direction (closkwise ot counter clcokwise)
F) t = L/Vox = 0.33/4.5*10^6 = 7.333*10^-8 s or 73.33 ns
G) Time periode = 2*pi*m/B*q
= 2*pi*9.1*10^-31/(8.02*10^-3*1.6*10^-9)
= 4.456 ns
let n is the no of rotations made
n = t/T = 73.33 ns/4.456ns = 16.5 revolutions
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