William C. answered • 09/14/23
Experienced Tutor Specializing in Chemistry, Math, and Physics
First we determine the magnetic force.
Magnetic Force
F = |q|(v)(B)(sinθ)
The magnetic force depends on the angle between the magnetic field vector and the velocity vector of the charged particle (an electron in this case). The sinθ term in the formula takes this angle into account. Note that the magnitude of the force is at a maximum when θ = ±90° and drops to zero at θ = 0° or 180°.
BTW, this is the stage where the advised sketch would be useful.
Acceleration
a = F/m = |q|(v)(B)(sinθ)/m
Acceleration is just force divided by mass of the electron.
where
|q| = 1.6 × 10–19 C is the absolute value of the charge of an electron
v = 0.867 x 106 m/s (given)
B = 0.01 T (given)
sinθ = sin(90 + 54.7) = sin(144.7) = 0.578
m = 9.11 × 10–31 kg is the mass of an electron
As long as we are careful to express everything above in SI units, we can just plug the numbers into the formula above to calculate acceleration.
Answer
a = F/m = (1.6 × 10–19)(0.867 x 106)(0.01)(0.578)/(9.11 × 10–31) = 8.8 × 1014 m/s2
William C.
You're right. The set up is correct, but I made a couple of dumb, careless mistakes with the numbers that I plugged into the calculation. I used O.1T instead of 0.01T for the magnetic field and I put the magnetic field on the negative x-axis instead of the negative y-axis which led to the wrong angle for the calculation of sinθ. These are errors are fixed, which I think should should lead to the correct answer.09/15/23
Awo G.
that's wrong09/14/23