4.18 An infinite line current carrying a dc with amplitude I. (flowing out of the page), passing through the point (s,d,0) in front of a cornered infinite ground planes defined by the xz- plane and the yz-plane as shown. Find the magnetic (B) field at any location (x,y,z) in front of the ground planes. Also calculate the surface current density on the xz-plane (y=0). O GROUND y air S d X

a) A circular loop of radius ? carries current ? as shown in the figure. Find the magnetic flux density ?⃗ at a point on the axis of the loop by using Biot-Savart law. Show all the details of Biot-Savart formulation b) A surface charge density exists on the hemispherical surface of the radius ? shown in the figure given as??⃗⃗ =?0????ê?A/m where ?0 is constant. i) Find the total current flowing on the surface ii) Using the solution of part (a), find the magnetic flux density ?⃗ at the origin ?.

A long, cylindrical wire has the cross-section of an annulus, i.e. region between twoconcentric circles, see the shaded area in figure a). The outer radius of the wire is 2R, the innerdiameter is R. Current I flows along the wire (perpendicularly into the page) in uniform distributionbetween radii R and 2R. 1)Find and plot the magnitude of the magnetic field as a function of distance r from thesymmetry axis of the wire.2) Suppose now that the cavity of radius R is not coaxial with the outer surface of the wire, asseen in figure b). Find the magnetic field at point P located in the center of the cavity. The currentdistribution in the wire is assumed to be uniform, the value of current is I.

This is a practice problem from the Engineering Electromagnetics course in my Electrical Engineering program. Could you please walk me through the steps of solving it so that I can solve more complicated ones in the future? Thank you for your assistance.

Plane z = 0 separates air and metal. Air is at z < 0 and the metal is at z 2 0. Given the permeability of air is , and that of the metal is u=135 u,.If the magnetic field intensity in air is H =125â, +140â, - 50â, A/m, find the magnetic flux intensity, B in the metal and the angle formed at the interface. Then, Illustrate through figure representation how plane z can separating air and metal. Given : 4, = 47 x 10- H/m and & 10-9-7 F/m %3D 36л

A wire carrying a current /= 27.0 A is bent into the shape of an exponential spiral. Its polar coordinate is described by r = exp(0) from 0-0 to 0-2 as shown in the figure. dr ds B-x/4 To complete the loop, the ends of the spiral are connected by a straight wire along the x axis. Find the magnitude of the magnetic field B at the origin. Suggestions: Although this problem may look daunting at first, remember that the Biot-Savart law is a good starting point to find the magnetic field due to a given current distribution. The simple exponential dependence of the path on the angle should give rise to an integral that is easy to solve. Also, it may help to know that the angle ẞ between a radial line and its tangent line at any point on the curve r = f(0) is related to the function in the following way: tan(B) dr di Thus, in the case of r = exp(0), tan(B)=1 and ẞ=4. Therefore, the angle between the line element vector ds and the radial unit vector r^ is -ẞ=. Additionally, this gives: dr…

One end of a conducting bar sits on a circular rail and the other end is fixed to point P such that the bar is able to rotate. A steady and uniform magnetic field B is directed into the page. If the bar is rotated about point P in a clockwise direction, the direction of the induced current though the resistor R is x, a O from a to b. O from b to a. O No current is induced.

A circular loop made of a stretched conducting elastic material has a 1.23 m radiusand is placed in a uniform magnetic field of 785 mT. The direction of the area ofloop plane is perpendicular to the magnetic field. When stretching of the loop isreleased, the radius of the loop starts to decrease at an instantaneous rate of7.50 cm/s. Calculate the emf induced in the loop at that instant.

Please explain in detail. Thanks!

A steady current ? flows down a long cylindrical wire of radius ?. Find the magnetic field both inside and outside if,a) The current is uniformly distributed over the outside surface of the wire. b) The current is distributed in such a way that ? is proportional to ?, the distance from the axis.  check the image, explain step by step.