Final answer:
To find the electron's speed moving at right angles to a magnetic field experiencing a known acceleration, we use the formula for the magnetic force on a charged particle in motion, which when equated to the centripetal force, leads us to the velocity of the electron.
Step-by-step explanation:
The student's question revolves around determining the speed of an electron moving at right angles to a given magnetic field, when the electron experiences a known acceleration. When a charged particle like an electron moves perpendicular to a magnetic field, it experiences a force perpendicular to both the velocity and the field. This scenario typically results in the particle undergoing uniform circular motion. In such a motion, the magnetic force is the centripetal force that causes the electron to accelerate towards the center of the circular path it follows.
The magnitude of the magnetic force (F) on a charged particle moving in a magnetic field is given by:
F = qvBsin(θ),
where 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 direction. For motion perpendicular to the field, θ is 90 degrees (π/2 radians), making sin(θ) equal to 1.
Since the electron is moving in a circular path, the magnetic force is also the centripetal force (Fc) required to keep the electron in circular motion, which can be expressed as:
Fc = mv2/r,
where m is the mass of the particle, v is its velocity, and r is the radius of the circular path.
Given the acceleration of the electron (a = 5.9 × 1015 m/s2), which in the case of circular motion is equal to the centripetal acceleration (ac), we can equate Fc with mv2/r and substitute ac for v2/r, giving us:
Fc = mac,
and using the first equation for magnetic force,
qvB = ma.
Since we are looking for the velocity (v), we can solve for v:
v = a/qB.
For an electron, q is the elementary charge, which has a magnitude of 1.60 × 10−19 C. We can now plug in our values:
v = (5.9 × 1015 m/s2) / ((1.60 × 10−19 C) × 0.17 T).
After calculating, we would get the electron's speed.