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 dB 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

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) =

In a given region of space, the vector magnetic potential is given by A = x5 coszy + z(0.2+ sin zx) mWb/m. The magnetic flux passing through a square loop with 0.25 cm long edges if the loop is in the x-y plane, its center is at the origin, and its edges are parallel to the x- and y- axis?

An infinite length line carries current I in the +az direction on the z-axis, and this is surrounded by an infinite length cylindrical shell (centered about the z-axis) of radius a carrying the return current I in the -az direction as a surface current. Find expressions for the magnetic field intensity everywhere. If the current is 1.0 A and the radius a is 2.0 cm, plot the magnitude of H versus radial distance from the z-axis from 0.1 cm to 4 cm.

Consider the cylindrical conductor with a hollow center and copper walls of thickness b-a as shown. The radii of the inner and outer walls are a and b respectively. and the current I is uniformly spread over the cross section of the copper (shaded region). What is the magnitude of the magnetic field in units of nT at r- 24.1cm. a=13cm, b=30.5cm, 7- 200mA, Hom4 x 10 Tm/A. Provide your answer with two decimal places. A -- 01 (out of page)

The set up is shown in the figure, where 25 A is flowing in the wire segments, AB = CD = 36 m, and the wire segment arc has a radius 33 m subtending an angle of 90◦. The permeability of free space is 1.25664 × 10^−6 T · m/A. Find the magnitude of the magnetic field at O due to the current segment ABCD.Answer in units of T.

Three long, parallel conductors each carry a current of I = 2.40 A. The figure below is an end view of the conductors, with each current coming out of the page. Taking a = 1.20 cm, determine the magnitude and direction of the magnetic field at the following points.   (a) point A magnitude  µT direction          (b) point B magnitude  µT direction          (c) point C magnitude  µT direction