An electron experiences a force F = (2.9 i - 2.7 j) 10-13 N when passing through a magnetic field B = (0.18 T) k. Determine the electron's velocity. I ain't too good with vectors, can someone help me out? The forumla is F = qv X B or F = qvBsin(theta) How can I find the angle between the magnetic field (B) and the unknown velocity?
the dot product between two vectors is equal to the product of the magnitudes of the two vectors times the cosine of the angle betwixt them. If you're serious about pursuing physics as a career, the best thing you could possibly do for yourself is develop a strong understanding of linear algebra and vectors. It would behoove you to begin delving into that early to get a nice advantage over everyone else, and linear algebra is probably the easiest branch of mathematics I've encountered so far.
So you are saying the dot product of the F and B vectors = product of their mags x cose of the angle between them? What about the velocity?
The dot product is indeed like what you said, however it is irrelevant here since in the Lorentz force, it is the cross product whch is involved. The magnitude of the cross product between two vectors is the product of the magnitudes of the two vectors time the sine of the angle between them. The direction of the cross product is perpendicular to the plane defined by the two vectors. Finally, in order to chose between the two possible directions, you use the right hand rule.
The formula F = qvBsinθ is only for the magnitude of the force. You should use the vector formula F = qv x B. In order to find the velocity, you should write the components of this equation: F<sub>x</sub> = qv<sub>y</sub>B<sub>z</sub> - qv<sub>z</sub>B<sub>y</sub> F<sub>y</sub> = qv<sub>z</sub>B<sub>x</sub> - qv<sub>x</sub>B<sub>z</sub> F<sub>z</sub> = qv<sub>x</sub>B<sub>y</sub> - qv<sub>y</sub>B<sub>x</sub> In the example you gave, you have q = -1.6 10<sup>-19</sup>C; F<sub>x</sub> = 2.9 10<sup>-13</sup>N;F<sub>y</sub> = -2.7 10<sup>-13</sup>N;F<sub>z</sub> = 0;B<sub>x</sub> = 0;B<sub>x</sub> = 0 and B<sub>z</sub> = 0.18 T. Just replace the numbers in the equations and solve them in order to find the components of the velocity, Remark: You will find that in fact you will not have any equation for v<sub>z</sub>. Before I explain why, try first to think by yourself why is that? If you don't find why, I'll explain it later, Then retry to solve it with the formula for the magnitude.
