PRACTICE IT Use the worked example above to help you solve this problem. A certa
ID: 1492180 • Letter: P
Question
PRACTICE IT
Use the worked example above to help you solve this problem. A certain solenoid consists of 138 turns of wire and has a length of 10.1 cm.
(a) Find the magnitude of the magnetic field inside the solenoid when it carries a current of0.620 A.
? T
(b) What is the momentum of a proton orbiting inside the solenoid in a circle with a radius of0.023 m? The axis of the solenoid is perpendicular to the plane of the orbit.
? kg · m/s
(c) Approximately how much wire would be needed to build this solenoid? Assume the solenoid's radius is 6.19 cm.
? m
EXERCISEHINTS: GETTING STARTED
Suppose you have a 31.6 m length of copper wire. If the wire is wrapped into a solenoid 0.240 m long and having a radius of 0.0449 m, how strong is the resulting magnetic field in its center when the current is 12.6 A?
B = T
Explanation / Answer
PRACTICE IT
a) B = mue*N*I/L
= 4*pi*10^-7*138*0.62/0.101
= 1.06*10^-3 T
b)
we know, r = m*v/(B*q)
r = P/(B*q)
==> P = r*B*q
= 0.023*1.06*10^-3*1.6*10^-19
= 3.9*10^-24 kg.m/s
c) length of the wire needed = N*2*pi*r
= 138*2*pi*0.0619
= 53.7 m
GETTING STARTED
No of turns, N = 31.6/(2*pi*0.0449)
= 112
L = 0.24 m
B = mue*N*I/L
= 4*pi*10^-7*112*12.6/0.24
= 7.4*10^-3 T
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