Final answer:
The magnitude of the magnetic force on a charged particle in a magnetic field is determined using the formula F = qvBsinθ. To find the angle θ for an electron in a known magnetic field, rearrange the formula and calculate θ, considering the electron's charge and the sine function's range, yielding two possible angles.
Step-by-step explanation:
The magnitude of the magnetic force exerted on a charged particle moving through a magnetic field can be calculated using the formula F = qvBsinθ, where q represents the charge of the particle, v is the velocity at which the particle moves, B is the magnetic field strength, and θ is the angle between the velocity vector and the magnetic field vector. In this specific scenario, given an electron moving at velocity 4.00 × 10³ m/s within a magnetic field of strength 1.25-T, experiencing a force of 1.40 × 10⁻¹⁶ N, we need to find the angle θ. Re-arranging the formula to solve for θ, we use the equation θ = arcsin(F/(qBv)). First, we can find the charge of the electron, which is known to be -1.60 × 10⁻¹⁹ C. Plugging our values into the formula we get θ = arcsin((1.40 × 10⁻¹⁶ N)/((-1.60 × 10⁻¹⁹ C) · (4.00 × 10³ m/s) · (1.25 T))).
Calculating the value of sine, we find two possible angles between the velocity of the electron and the magnetic field as this is an inverse sine function which spans two quadrants with positive sine values. The two possible answers for θ would be in the first and the second quadrants.