Respuesta :
Answer:
r4 > r2 > r3 > r1
Explanation:
correction of the statement:
The particles have the following masses and charges:
1 : charge q; velocity v and mass m
2: charge 2q velocity 2v and mass 2m
3: charge q: velocity 3v, mass m/2
4: charge 2q: velocity 3v, mass 2m
In order to calculate the radius of the trajectories of the four particles, you use the following formula for the radius of the trajectory of a particle in a perpendicular and constant magnetic field:
[tex]r=\frac{mv}{qB}[/tex] (1)
m: mass of the particle
v: speed of the particle
q: charge
B: magnitude of the magnetic field
Then, in comparison with the equation (1), you obtain for each case:
1 : charge q; velocity v and mass m
[tex]r_1=\frac{mv}{qB}[/tex] = r
2: charge 2q velocity 2v and mass 2m
[tex]r_2=\frac{(2m)(2v)}{(2q)B}=2\frac{mv}{qB}=2r[/tex]
3: charge q: velocity 3v, mass m/2
[tex]r_3=\frac{(m/2)(3v)}{qB}=\frac{3}{2}\frac{mv}{qB}=\frac{3}{2}r[/tex]
4: charge 2q: velocity 3v, mass 2m
[tex]r_4=\frac{(3v)(2m)}{(2q)B}=3\frac{mv}{qB}=3r[/tex]
By the previous results you can conclude:
r4 > r2 > r3 > r1
The ranking of radii of their paths for these particles, largest to smallest is r4 > r2 > r3 > r1.
The radius of the trajectories:
For determining it we use the following formula that should be perpendicular and contained the magnetic field:
r = mv/qB
here,
m: mass of the particle
v: speed of the particle
q: charge
B: magnitude of the magnetic field
Now, for the charge 1
r1 = m * v/(B * q)
for the charge 2
r2 = 2m * 2v/(2Bq) = 2 * mv/Bq
for the charge 3
r3 = 3/2 * mv/(B*q)
for the charge 4
r4 = 6 mv/(2 * B * q) = 3 mv/(B*q)
hence, the ranking of the radii is r4 > r2 > r3 > r1
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