Question

# A single loop of wire of radius 12 cm lies on the x-y plane (imaging it...

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. 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

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