Magnetic Field of a Coil Problem

[bdh2991]

Homework Statement

a positive point charges q= +8.00 μc and q'= +3.00μc are moving relative to an observer at point p (midway between the charges) the distance from on charge to the point is .12 m and one charge moves to the right at 4.5 x 10^6 m/s while the other moves to the left at 9.00 x 10^6 m/s. when the two charges are at the locations described , what are the magnitude and direction of the magnetic field they produce at point P??

Homework Equations

B = (μqv X r)/(4∏r^3)

where μ is the constant 4∏ x 10^-7, and v X r is the cross product

The Attempt at a Solution

I broke it down into two separate magnetic fields

for the first one I did the cross product of v and r and got 5.4 x 10^6 in the -k direction
then plugged it into the formula and got 2.5 x 10^-6 -k, for the magnetic field

for the second one i did the same thing and with the cross product i got 1.08 x 10^7 -k,
and after plugging that in i got 1.875 x 10^-6 -k

when i added them together i got 4.375 x 10^-6 in the -k direction but the books answer says that the magnetic field is directed into the page...

i never remember using a right-hand rule for these type of problems so am i just supposed to assume that the -k direction is always into the page?

 

[Redbelly98]

It is conventional for the +k (or +z) direction to equal i×j. This is also known as a "right-handed coordinate system", since the right hand is used to find the direction of i×j.

The result is that, if +x is to the right and +y is up toward the top of the page, then +z is out of the page and -z is into the page. Hope that makes sense for the problem you are working on here.