Please help with part C! The answer is NOT 1=2=3 Thanks!! The figure below shows
ID: 1777248 • Letter: P
Question
Please help with part C! The answer is NOT 1=2=3 Thanks!!
The figure below shows the paths flowed by three charged particles through a region of uniform magnetic field that is directed perpendicular to the page. The particles have the same mass, and their charges have the same magnitude. The paths of particles 1 and 2 represent one quarter of a circle, while that followed by particle 3 is a half circle. (a) Rank these particles, from largest to smallest, based on their speed. (Use only ">"or"symbols. Do not include any parentheses around the letters or symbols.) 2-1>3 (b) Rank these particles, from largest to smallest, based on the magnitude of the magnetic force they experience in this region. (Use only">" or"symbols. Do not include any parentheses around the letters or symbols.) 2 1>3 (c) Rank the particles based on the time they spend passing through the region shown in the picture, from argest to smallest. (Use only ">"orsymbols. Do not include any parentheses around the letters or symbols.)Explanation / Answer
given, region of uniform magnetic field
particles have same mass m, same charge magnitude q
now, for a charged particle of mass m moving with speed v
qvB = mv^2/R [ where R is radius of the circle followed by the particle in the uniform magnetic field B]
hence
mv/qB = R
a. ranking from largest to smallest based on speed
v = RqB/m
m is same for all particle3s and so is q and B
so v is proiportional to R
from the diagram
R2 > R1 > R3
hence
2 > 1 > 3
b. based on magnertic force from largest to smallest
magnetic force = qvB
as q and B is same for all particles
2 > 1 > 3
c. time spent passing throught thje region = distance/speed
so from diagram
R1 = 2
R2 = 3
R3 = 1
so, v1 = 2k [ where k = qB/m]
v2 = 3k
v3 = k
so t1 = 2*pi*R1/4*v1 = pi/2k
t2 = 2*pi*R2/4v2 = pi/2k
t3 = 2*pi*R3/2v3 = 2*pi*1/2*k = pi/k
hence
t3 > t2 = t1
3 > 2 = 1