Math Problem Statement
A beam of protons moves at 459005 m/s through a uniform 1.3 T-magnetic field directed along the positive z-axis. The velocity of each proton lies in the xz-planes and is directed at 40 rad to the +z-axis. Find the force on a proton.
Solution
To find the force on a proton moving in a magnetic field, we can use the following formula for the magnetic force on a charged particle:
where:
- is the charge of the proton (),
- is the velocity of the proton,
- is the magnetic field strength,
- is the angle between the velocity vector and the magnetic field direction.
Given Data
- (we will use this angle in radians directly, as it's provided as 40 radians).
Note: However, an angle in the context of a physical system is typically expressed in degrees or radians within the range radians. Since 40 radians is far beyond this, let's proceed assuming you meant for practical accuracy. Thus:
-
Convert the angle to radians if needed (assuming it's 40 degrees):
-
Calculate the force:
Let’s compute this explicitly:
Answer
The force on a proton in the given conditions is approximately:
Would you like more details on any part of this calculation?
- What happens to the force if the angle changes?
- How would the force change if the magnetic field strength increased?
- What if the proton’s velocity was doubled?
- How is the direction of the force determined?
- What role does the proton’s charge play in this formula?
Tip: Remember, the force is always perpendicular to both the magnetic field and the velocity direction, following the right-hand rule.
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Math Problem Analysis
Mathematical Concepts
Magnetic Force
Vector Calculations
Trigonometry
Formulas
F = q v B sin(θ)
Theorems
Right-Hand Rule for Magnetic Force
Suitable Grade Level
Grades 11-12
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