One beam of electrons moves at right angles to a magnetic field. the force on these electrons is 4.9 × 10-14 newtons. a second beam travels at the same speed, but at a 30° angle with the magnetic field. what force is on these electrons?

a.(4.9 × 10-14 newtons) · tan(30°)
b.(4.9 × 10-14 newtons) · sin(30°)
c.(4.9 × 10-14 newtons) · cos(30°)
d.(4.9 × 10-14 newtons) · arctan(30°)
e.(4.9 × 10-14 newtons) · arccos(30°)

B.(4.9 × 10-14 newtons) · sin(30°)

Explanation:

The magnetic force exerted on charged particles by a magnetic field is given by

where

q is the charge

v is the speed of the charge

B is the magnetic field intensity

is the angle between the direction of v and B

The first beam moves at right angle to the magnetic field, so and the force on this beam is simply

(1)

The second beam moves at angle of . The electrons are travelling at same speed v, and the magnetic field is still the same (and the charge q is also the same, since they are electrons as well), so the magnetic force in this case is

(2)

But from the previous equation we know that

so, if we substitute into eq. (2), we find

pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y