Magnetic force, finding angle between velocity and magnetic field (2024)

Homework Statement

a 3 microcoulomb charge having a speed of 10m/s is fired into a region of constant magnetic field where B is given by:

B = 0.3i - 0.4j

a) the magnitude force on the charge is found to be 2*10^-6 Newtons. what is the angle between v and B?

b) if the direction of v is changed so that the charge moves along the +z direction at a speed of 10m/s, what would be the magnitude and direction of the magnetic force in this case?i am supposed to get 7.66 degrees for part a, and 15*10^-6 Newtons at 36.9 degrees for part b

Homework Equations

radius r = mv/qB where m is mass, v is velocity, q is charge, B is magnetic field

electromagnetic force, F = qE + qv X B where X indicates cross product, E is electric field

The Attempt at a Solution

part a:

using F = qE + qv X B ----> find theta
F = qE + qv X B
2*10^-6 = (3*10^-6E) + ((3*10^-6)(10)(0.3i - 0.4j)sin(theta))
sin(theta) = 2*10^-6 - 3*10^-6E/((3*10^-6)(10)(0.3i - 0.4j))
theta = inverse sin((2*10^-6 - 3*10^-6E)/(9*10^-6i - 1.2*10^-5j)) holding electric field E constant

is this the correct approach to find theta?

i haven't started part b yet, but i am assuming theta changes to (theta from part a + 90 degrees) and i just substitute that new theta into the electromagnetic force equation to solve for force.

is my approach for part a, correct? how about part b? or am i using the wrong equation?

i am supposed to get 7.66 degrees for part a, and 15*10^-6 Newtons at 36.9 degrees for part b

any help appreciated

hint: the magitude of v is already given, you have to calculate the magnitude of B then find theta by:
F = q(v X B) = q|v||B|sin(theta)

hope this helps

fizikx

oh you a right, that equation was right in front of me, must've forgotten.

F = qvB sin(theta) --> find theta
2*10^-6 = (3*10^-6)(10)(0.3i -0.4j) sin(theta)
sin(theta) = (2*10^-6)/(9*10^-6i - 1.2*10^-5j)
theta = inverse sine [(2*10^-6)/(9*10^-6i - 1.2*10^-5j)]
theta = inverse sine[(2*10^-6)/(-3*10^-6)]
theta = inverse sine(-0.667)
theta = -41.83 degrees

i must've done something wrong with the denominator in terms or i and j. i am supposed to get 7.66 degrees. what do i need to fix?

as for part b, how will the fact the charge moves along the +z axis, affect the components of the given magnetic field B?