Simplifying Lorentz Force Formula

[RobertL]

Hey everyone, I'm trying to make sure I did this question right. Any ideas would be greatly appreciated. Thanks!

Homework Statement

The general force that bends the electron in the e/m experiment is known as the Lorentz force, F = q(E + v x B), where force F, electric field E, velocity v, and magnetic field B are vectors, and x stands for the vector product. Given that there is no electric field, and the velocity vector is at an 45° angle with respect to the magnetic field, the formula for the Lorentz force experienced by a particle carrying electric charge q is which of the following:

qvB/2
qvB
qvB/sqrt(2)
qv/B

Homework Equations

F = q(E + v x B)

The Attempt at a Solution

I thought, as it was at a 45 degree angle, the qvB/sqrt(2) would be accurate as a right triangle with a 45 degree angle creates a hypotenuse of sqrt(2)

 

[tiny-tim]

Hey RobertL!

F = q(E + v x B)

… the velocity vector is at an 45° angle with respect to the magnetic field
…
I thought, as it was at a 45 degree angle, the qvB/sqrt(2) would be accurate as a right triangle with a 45 degree angle creates a hypotenuse of sqrt(2)

Forget about right triangles.

The cross product means sin of the angle, and so it's sin 45° which is 1/√2.

 

[jambaugh]

Robert,
Your reasoning is correct as far as selecting the correct answer from an offered set but to get the most understanding of the material from this problem as possible, you should work on finding the answer for arbitrary numbers. If it were 33° instead can you write down the answer? Hence tiny-tim's comments.