Final answer:
The angle θ between the velocity of an electron and a magnetic field, given a known force, can be calculated using the magnetic force formula. There are two possible angles due to the sin(θ) function, and these can be calculated using the inverse sine of the force divided by the product of the charge, velocity, and magnetic field.
Step-by-step explanation:
The question relates to the magnetic force and magnetic fields, and how these affect electron trajectories. To find the angle that the velocity of an electron makes with a magnetic field when a known force is experienced, we use the formula for magnetic force on a moving charge: F = qvBsin(θ), where F is the force, q is the charge, v is the velocity, B is the magnetic field, and θ is the angle between the velocity and the direction of the magnetic field. Given the force (1.40 × 10-16 N), the charge of an electron (approximately -1.60 × 10-19 C), the velocity (4.00 × 103 m/s), and the magnetic field (1.25 T), we can solve for θ, finding there are two possible angles due to the sin(θ) function.
To solve for θ, we rearrange the formula to θ = arcsin(F / (qvB)). Plugging in the values gives us θ = arcsin((1.40 × 10-16N) / ((1.60 × 10-19C) × (4.00 × 103m/s) × (1.25 T))). Calculating this will give us the two possible angles at which the velocity vector of the electron is oriented with respect to the magnetic field.