If the magnetic field strength is doubled, what happens to the magnetic force on a charged particle moving perpendicular to the field?
Practice Questions
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Q1
If the magnetic field strength is doubled, what happens to the magnetic force on a charged particle moving perpendicular to the field?
Doubles
Halves
Remains the same
Quadruples
The magnetic force on a charged particle is given by F = qvB sin(θ). If the magnetic field strength B is doubled, the force F also doubles, assuming charge q and velocity v remain constant.
Questions & Step-by-step Solutions
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Q
Q: If the magnetic field strength is doubled, what happens to the magnetic force on a charged particle moving perpendicular to the field?
Solution: The magnetic force on a charged particle is given by F = qvB sin(θ). If the magnetic field strength B is doubled, the force F also doubles, assuming charge q and velocity v remain constant.
Steps: 7
Step 1: Understand the formula for magnetic force, which is F = qvB sin(θ).
Step 2: Identify the variables in the formula: F is the magnetic force, q is the charge of the particle, v is the velocity of the particle, B is the magnetic field strength, and θ is the angle between the velocity and the magnetic field.
Step 3: Note that in this case, the particle is moving perpendicular to the magnetic field, so θ = 90 degrees.
Step 4: Since sin(90 degrees) = 1, the formula simplifies to F = qvB.
Step 5: If the magnetic field strength B is doubled, we replace B with 2B in the formula: F = qv(2B).
Step 6: This means the new force F' = qv(2B) = 2(qvB), which shows that the force F' is double the original force F.
Step 7: Therefore, if the magnetic field strength is doubled, the magnetic force on the charged particle also doubles.
