Path diameter difference of two singly-charged ions in a magnetic field

In summary, the path diameter difference of two singly-charged ions in a magnetic field refers to the difference in the curvature of their paths as they travel through the field. This is calculated using the equation Δd = qBv/m, which takes into account the strength of the magnetic field, velocity, and mass and charge of the ions. The path diameter difference can affect the interactions between the ions and has various applications in fields such as particle physics and technology like mass spectrometry.
  • #1
fight_club_alum
63
1
Homework Statement
Two single charged ions moving perpendicularly to a uniform magnetic field (B = 0.4 T)
with speeds of 5000 km/s follow circular paths that differ in diameter by 5.0 cm. What is
the difference in the mass of these two ions?
a . 2.6 × 10–28 kg
b. 6.4 × 10–28 kg
c. 3.2 × 10–28 kg
d. 5.1 × 10–28 kg
e. 1.1 × 10–28 kg
Relevant Equations
MV/Qb = r
M1(50,000)/q (0.4) - M2(50,000)/q (0.4) = 0.025

Is there a special charge for singly charged ions?
 
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  • #2
fight_club_alum said:
Problem Statement: Two single charged ions moving perpendicularly to a uniform magnetic field (B = 0.4 T)
with speeds of 5000 km/s follow circular paths that differ in diameter by 5.0 cm. What is
the difference in the mass of these two ions?
a . 2.6 × 10–28 kg
b. 6.4 × 10–28 kg
c. 3.2 × 10–28 kg
d. 5.1 × 10–28 kg
e. 1.1 × 10–28 kg
Relevant Equations: MV/Qb = r

Is there a special charge for singly charged ions?
Ask yourself what an ion being singly charged means. What happens to form an ion?
 

Related to Path diameter difference of two singly-charged ions in a magnetic field

1. What is the path diameter difference of two singly-charged ions in a magnetic field?

The path diameter difference of two singly-charged ions in a magnetic field refers to the difference in the curvature of their paths as they move through the field. This is due to the interaction between the ions' charges and the magnetic field, causing them to follow curved paths instead of straight lines.

2. How is the path diameter difference of two singly-charged ions affected by the strength of the magnetic field?

The path diameter difference is directly proportional to the strength of the magnetic field. This means that as the strength of the field increases, the curvature of the paths of the ions also increases, resulting in a larger path diameter difference.

3. Does the mass of the ions affect the path diameter difference in a magnetic field?

Yes, the mass of the ions does affect the path diameter difference. Heavier ions will have a smaller path diameter difference compared to lighter ions due to their larger inertia, which makes it more difficult for the magnetic field to affect their paths.

4. Can the path diameter difference be calculated mathematically?

Yes, the path diameter difference can be calculated using the equation: ΔD = qVB²/2m, where q is the charge of the ions, V is the velocity, B is the strength of the magnetic field, and m is the mass of the ions.

5. How is the path diameter difference of two singly-charged ions in a magnetic field useful in scientific research?

The path diameter difference is useful in studying the behavior and properties of charged particles in a magnetic field. It can also be used in various applications such as in particle accelerators, mass spectrometry, and plasma physics research.

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