A 2.40 cm x 2.40 cm square Ampèrian loop exists in the xy plane in a region of space with a magnetic field. The magnetic field has a y component that varies along the x direction and an x component that varies along the y direction as described by B = (0.105yi - 0.105xj) T. Calculate the contribution to the circulation integral due to each segment of the loop, and determine the net current through the loop that must be present. (Assume that the lower left corner of the loop is at the origin of the xy plane. Enter che magnitudes.) T.m (top segment) T. m (right segment) T.m (bottom segment) T.m (left segment) Ithni = A

Figure (a) shows an element of length ds = 1.26 um in a very long straight wire carrying current. The current in that element sets up a differential magnetic field aB at points in the surrounding space. Figure (b) gives the magnitude dB of the field for points 3.6 cm from the element, as a function of angle between the wire and a straight line to the point. The vertical scale is set by dB = 60.0 pT. What is the magnitude of the magnetic field set up by the entire wire at perpendicular distance 3.6 cm from the wire? Number i Units dB (pT) dB₂ 0 μT (a) π/2 9 (rad) (b) Wire 2

At a particular point on Earth, the magnitude of the Earth's magnetic field is 3.50 x 10-5 T. At this point, the field through a small square loop is essentially uniform. The area of the loop is 30.0 cm2. What is the magnitude of the magnetic flux (in T: m2) through the loop when the loop is at the following orientations? (a) the magnetic field is perpendicular to the plane of the loop 1.05*10**-3 X T. m2 (b) the magnetic field and the normal to the plane of the loop are at a 20.0° angle 6.68*10**-8 T.m2 (c) the magnetic field and the normal to the plane of the loop are at a 90.0° angle T.m?

A conducting cylinder has radius ?a and volume current density J1=κr in the direction of the axis of the cylinder where κ is known.  It is coaxial with a conducting cylindrical shell which has inner radius b and outer radius c.   Suppose we have already determined that the magnetic field outside both cylinders is zero.  If the outer cylinder has a current density of J2=αr, find α.   Find the magnetic field in each possible region   B(r<a) =   B(a<r<b) =   B(b<r<c) =