Acurrent filament carrying 15a in the ax direction lies along the entire x- axis. find h in rectangular system at point(2,1,0)

H=(0,0,2.39)A/m

Explanation:

Ampere's Law for a current filament:

H*(2*pi*R)=I ⇒ H=I/(2*pi*R)

in this case R=y=1; because the current is in the axis x

H=I/(2*pi)=15/(2*pi) A/m=2.39A/m; magnitude

the vector:

to find the direction of the magnetic force H, we uses the right hand rule

H=(0,0,2.39)A/m

what was the answer?

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west