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## Homework Statement

A group of particles is traveling in a magnetic field of unknown magnitude and direction. You observe that a proton moving at 1.50 km/s in the +x-direction experiences a force of 2.25 x ##10^{-16}##N in the +y-direction, and an electron moving at 4.75 km/s in the -z-direction experiences a force of 8.50 x ##10^{-16}##N in the +y-direction. a) What are the magnitude and direction of the magnetic field?

## Homework Equations

Right hand rule

F = |q|vB

##\vec F = qv##x##\vec B##

## The Attempt at a Solution

info for proton:

##m_1 = 1.6727 * 10^{-27} kg##

##q_1 = +1.602 * 10^{-19} C##

##\vec v_1 = 1500 m/s## in the +x direction.

##\vec F_1 = 2.25 * 10^{-16} N## in the +y direction.

info for the electron:

##m_2 = 9.110 * 10^{-31} kg##

##q_2 = -1.602*10^{-19} C##

##\vec v_2 = 4750 m/s## in the -z direction

##\vec F_2 = 8.50 * 10^{-16} ## in the +y direction

,i'm pretty sure I solved for B correctly incase you want to skip this part..

##\vec B = <b_1, b_2, b_3>##

then i do cross product to solve for the B components.

first equation, for proton:

##<0, 2.25 * 10^{-16}, 0> = q<1500, 0, 0>##x##<b_1, b_2, b_3>##

second equation, for electron:

##<0,8.50*10^{-16}, 0> = -q<0, 0, -4750>##x##<b_1, b_2, b_3>##

where ##q = +1.602*10^{-19}##

first equation simplifies to this:

##q<1500, 0, 0>##x##<b_1, b_2, b_3>##

##= q<0, -1500b_3, 1500b_2>##

## = <0, -1500b_3q, 1500b_2q##

second equation simplifies to this:

##-q<0, 0, -4750>##x##<b_1, b_2, b_3>##

##= -q<4750b_2, -4750b_1, 0>##

##= <-4750b_2q, 4750b_1q, 0>##

so now i have 2 equations:

##<0, 2.25 * 10^{-16}, 0> = <0, -1500b_3q, 1500b_2q##

##<0,8.50*10^{-16}, 0> = <-4750b_2q, 4750b_1q, 0>##

##b_3 = \frac {2.25*10^{-16}} {-1500q} = -.936##

##b_2 = 0##

##b_1 = \frac {8.50*10^{-16}} { 4750q} = 1.117##

##B = \sqrt {(-.936)^2 + (1.117)^2} = 1.46T##

now when i try to do the right hand rule.. i get confused

what i know is velocity direction is the thumb, force direction is the palm, and magnetic field direction are the fingers.

but there are 2 velocities and 2 forces... so i try to do it for both of them..

for the proton my thumb points toward me, my palm faces to my right, and so my fingers point toward the floor. So the magnetic field is South.

for the electron my thumb points toward the floor, my palm faces to my right, and so my fingers point away from me. So the magnetic field is in the -x direction.

How can I find the direction?