The picture below shows four square regions. Each of the four regions may have i
ID: 1537041 • Letter: T
Question
The picture below shows four square regions. Each of the four regions may have its own uniform magnetic field. If there is a uniform magnetic field in a region, the field is directed either into or out of the screen (or the page, if you printed your assignment out on paper). Two charged particles pass through this region. Particle 1 has a positive charge. The path of particle 1 is a quarter-circle in region A, a half-circle in region D, another quarter-circle in region A, and a quarter-circle in region B. The path of particle 2 is a straight line in region C, and a quarter circle in region D.
(b) Rank the four regions based on the magnitude of the magnetic field in the region, from largest magnitude to smallest magnitude. (Use only ">" or "=" symbols. Do not include any parentheses around the letters or symbols.)
(c) Assuming that the particles experience forces only from the magnetic fields, at which point does particle 1 have its largest kinetic energy? (select one)
before it enters region A for the first time
while it is in region A the first time
while it is in region D
while it is in region A the second time
while it is in region B
after it leaves region B
It has the same kinetic energy in all regions.
For the rest of this problem, use these numbers. Particle 1 has a charge of +30.0 microcoulombs, and a mass of 2.40 milligrams. Particle 1 also has a speed, when it enters region A, of 3.00 m/s.
(d) If region A is a square measuring 60.0 cm on each side (the other regions have the same size as region A, of course), what is the magnitude of the magnetic field in region A?
T
(e) From the instant particle 1 enters region A for the first time, until it leaves region B, how much time elapses?
s
(f) If particle 2 has the same mass and the same speed as particle 1, what is the charge on particle 2?
microcoulombs
Explanation / Answer
(a)
The magnetic field is directed out of the screen in region A.
The magnetic field is directed into the screen in region B.
There is no magnetic field in region C.
The magnetic field is directed into the screen in region D.
(b)
Observe the radius of curvarures of particle 1 in different regions
If the radius of curvature is large, the magnetic field in thar region is less
D > A > B > C
(c)
F = q*v*B*sin(theta)
Magnetic force acting on the charged particle only useful to change the direction of the particle to accelarate it
It has the same kinetic energy in all regions.
(d) the magnitude of the magnetic field in region A is
R = m*v/q*B
B = m*v/q*R
B = (2.4*10^-6*3.0)/(30*10^-6)*(0.20) T
= 0.048 T
(e) Time = distance/speed
= (pi*20+pi*10+pi/2*40)*10^-2/3
= 0.52 sec
(f) charge on particle 2
m*v^2/r= q*B
2.4*10^-6*9/0.40 = q*0.048
q = 2.5 microcoloumb
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