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

the answer is the first electromagnet (a). this is because it has more coils around the ferromagnetic material. increasing the number of coils increases the surface area in which the metal interacts with the current in the coil. this enables more atoms in the metal to become aligned hence becoming more magnetized.