We Can produce Current along a Wire by immersing it into a magnetic Vector field that is varying in time. Faraday's law relates the curl of the electric field E with changing magnetic field B as The magnetic field in 3-space is given by BO, y, = cr2i Where are the coordinates (according to a rectangular system) and t is time. The flux of the field through an immersed surface can be calculated as n=ffB.nas The change of the flux of the magnetic field with respect to time is equivalent to the work done by the electric current to circulate though the wire (shmvn in red colour in the figure below), i.e. At 5seconds using Faradayps law, calculate the work done to circulate the electric current through the closed wire, i.e. Work = The wire circulates the parl ofthe cone in the first octant, that is cut-offby the plane p3r+4 (see figure below). The curve C (shown in red) is circular, and it is the boundary of the surface S (shown in blue) that is the cut-off part of the cone by the plane p3r+4_ The normal of the surface S is oriented in the positive y-direction. That is; the orientation of the surface S is such that the y component of the normal is positive (rather than negative as either of the two can be selected as normal). The cone's tip point is at The Vector v. I-c.,7-c ,ll-c: is a position vector between the centre ofthe circle and the point R(l, 7, 1 1) . Direction ofthe vector v is parallel to the axis and its size is equal to the radius of the circle. rhe