Question

A single loop of wire of radius 12 cm lies on the x-y plane (imaging it lying on your page of paper) and carries a current of 1.00 A in the clockwise direction . At the same time, a long straight wire that just touches the rim at the edge of the wire loop carries a 0.808-amp current in the +z direction ("out of the page"). Find the magnetic field at the center of the wire loop. Reminder: the loop of wire and the straight wire both create a magnetic field, and both contribute to the magnitude of the net magnetic field at the center of the wire loop.

Answer 1

Magnetic field due to circular loop or wire is given by

B = uI/2R this is perpendicular to the plane of the loop

Now due the given loop it will be in negative Z from right hand screw rule

B = 4pi*10^-7*1.0/2(0.12m)(-k) = 5.236*10^-6(k)

And magntic field due to the long wire is given as

B = uI/2piR where R is the distance from the axis

B = 4pi*10^-7*0.808/2pi(0.12) (-i) (direction from right hand palm rule = 1.35*10^-6(-i)

Net B will be the resultant of both the fields

Net B = sqrt(B1^2+B2^2) =5.41*10^-6T