Final answer:
To calculate the magnitude of the acceleration of an electron in a magnetic field, first calculate the magnetic force using the Lorentz force equation, and then use Newton's second law to find the acceleration. The charge of the electron and the components of the magnetic field perpendicular to the electron's velocity are used in these calculations.
Step-by-step explanation:
The question asks what is the magnitude of the acceleration of an electron that has a velocity in a magnetic field with given components. To find the acceleration, the magnetic force on the electron needs to be calculated, which can be done using the Lorentz force formula, F = q(v × B), where F is the magnetic force, q is the charge of the electron, v is the velocity of the electron, and B is the magnetic field. The magnitude of the force F is given by |F| = |q| * |v| * |B| * sin(θ), where θ is the angle between the vectors v and B. The magnetic field components are perpendicular to the velocity of the electron, so θ is 90 degrees and sin(θ) is 1. The charge of an electron is –e, where e = 1.60 × 10⁻¹⁹ C. Thus, the force is F = |e| * v * Bₑ, where Bₑ is the component of the magnetic field perpendicular to v. Since the electron is moving in the x-direction and the x-component of the magnetic field does not contribute to the force, Bₑ can be found as √(Bₑ2 + Bz2) = √(1.52 + 2.02) T. The acceleration a can be found using Newton's second law, F = m * a, where m is the mass of the electron (9.11 × 10⁻1ⁱ kg). Solving for a, we have a = F/m. Plugging in the values, we can find the magnitude of the acceleration.