a solenoid that is 24cm long with a radius of 58.7mm carries a current of 6.50A.
ID: 1511290 • Letter: A
Question
a solenoid that is 24cm long with a radius of 58.7mm carries a current of 6.50A. the solenoid produces a magnetic field of 4.55mT. inside the solenoid a proton is orbiting in a circle with a momentum of 3.85x10-24kg m/sec. the axis of the solenoid is perpendicular to the plane of the orbit of the proton. Assume that the field inside the solenoid is uniform.
1. The approximate number of turns making up the solenoid is…
2. The length of wire needed to build this solenoid is…
3. The speed of the proton in its orbit inside the solenoid is…
4. The radius of the circular orbit of the proton in its orbit inside the solenoid is…
Explanation / Answer
L = 0.24 m
r = 58.7 * 10^-3 m
I = 6.50 A
B = 4.55 * 10^-3 T
(1)
Magnetic Field of solenoid is given by.
B = (uo*I*N)/L
4.55 * 10^-3 = (4**10^-7 * 6.5 * N)/0.24
N = 133.7
N = 134 Turns.
(2)
Length of the wire needed,
L = (2**r) * 134
L = 49.4 m
(3)
Momentum, P = 3.85 * 10^-23 Kg m/s
1.67 * 10^-27 * v = 3.85 * 10^-23
v = 2.31 * 10^4 m/s
(4)
m*v^2/r = q*v*B
(1.67 * 10^-27 * 2.31 * 10^4)/r = (1.6 * 10^-19 *4.55 * 10^-3 )
r = 0.053 m
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