How fast an H+ ion should move in a magnetic field 2.5 x 10^-3 T such that magnetic force equal its weight?
Correct answer: D. 4 x 10^-5 m/s
- A. 6 x 10^-5 m/s
- B. 4.5 x 10^-5 m/s
- C. 3.3 x 10^-6 m/s
- D. 4 x 10^-5 m/s
Explanation
To find the velocity at which the magnetic force equals the weight of the H+ ion, use the formula for magnetic force: Fmagnetic = evB, and set it equal to the gravitational force: Fgravity = mg.Equating the two forces gives: evB = mg. Solve for velocity v:v = mg/eBSubstituting the known values (where e is the charge of a proton, m is the mass of a proton, g is the acceleration due to gravity, and B is the magnetic field strength), we find:v ≈ 4 x 10-5 m/s.The other options either overestimate or underestimate the velocity required to balance the forces.
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Magnetic flux density and magnetic flux describe the strength of a magnetic field and the field passing through a surface. A charged particle moving through a magnetic field experiences a force perpendicular to its velocity and may follow circular or helical motion, depending on the angle between velocity and field.
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