The magnetic force acting on a straight wire carrying current I of length L in a uniform magnetic field B is given by F = IL x B, where L has length L and is pointing in the direction of the current. Consider the loop centered at the origin shown in the figure below. y= 4-x* for -24x42 -2 2 (b) The torque with respect to a pivot point is defined by the cross product of the separation vector i which is oriented from the pivot point to the point where the force acts and the force, チ=チxF. Find the torque acting on this loop with respect to the origin as the pivot point.

Two thin circular wires, each with radius a, carry equal currents I but in opposite directions. They are placed so that their centers are at z = ±a/2 and the plane of each loop is parallel to the xy- plane. Find the magnetic field at a point (0, 0, 2) on the symmetry axis. What is the magnetic dipole moment of the system? Expand B(z) for z ≫ a keeping the lowest order term in a/z.

A solenoid of radius r = 1.25 cm and length { 33.0 cm has 285 turns and carries 12.0 A. a (a) Calculate the flux through the surface of a disk-shaped area of radius R = 5.00 cm that is positioned perpendicular to and centered on the axis of the solenoid as in the figure (a) above. µWb (b) Figure (b) above shows an enlarged end view of the same solenoid. Calculate the flux through the tan area, which is an annulus with an inner radius of a = 0.400 cm and outer radius of b = 0.800 cm. µWb

A toroid is a solenoid bent into the shape of a doughnut. It looks similar to a toy Slinky® with ends joined to make a circle. Consider a toroid consisting of N turns of a single wire with current I flowing through it. (Figure 1) Consider the toroid to be lying in the re plane of a cylindrical coordinate system, with the z axis along the axis of the toroid (pointing out of the screen). Let represent the angular position around the toroid, and let r be the distance from the axis of the toroid. For now, treat the toroid as ideal; that is, ignore the component of the current in the direction. Figure 00 Ampèrean loop (a) 1 of 1 (b) Correct Notice that the direction is antiparallel to the path shown by the Ampèrean loop in the figure. Also, by definition, ✩ × î = Ô. Part C What is B (r), the magnitude of the magnetic field inside the toroid and at a distance r from the axis of the toroid? Express the magnetic field in terms of I, μo (the permeability of free space), N, and r. ► View…

Three long, straight wires are seen end-on in the figure below. The distance between the wires is r = 0.252 m. Wires A and B carry current IA = IB = 1.66 A, and wire C carries current Ic = 3.46 A. Assume (for example) the only forces exerted on wire A are due to wires B and C. Find the force per unit length exerted on the following. (Express your answers in vector form.) (a) wire A FA = B (b) wire B fB = IB A Ic c N/m N/m X

A metal rod of mass m slides without friction along two parallel horizontal rails, separated by a distance ℓ and connected by a resistor R, as shown in the figure below. A uniform vertical magnetic field of magnitude B is applied perpendicular to the plane of the paper. The applied force shown in the figure acts only for a moment, to give the rod a speed v. In terms of m, ℓ, R, B, and v, find the distance the rod will then slide as it coasts to a stop.   Note: See image for the original question and diagram.

A solenoid of radius r = 1.25 cm and length = 25.0 cm has 285 turns and carries 12.0 A. PLEASE DISREGARD FIGURE (b). R C b (a) Calculate the flux through the surface of a disk-shaped area of radius R = 5.00 cm that is positioned perpendicular to and centered on the axis of the solenoid as in the figure (a) above. μWb

A conducting bar of length ℓ moves to the right on two frictionless rails as shown in the figure below. A uniform magnetic field directed into the page has a magnitude of 0.330 T. Assume R = 8.70 Ω and ℓ = 0.390 m. A vertical bar and two parallel horizontal rails lie in the plane of the page, in a region of uniform magnetic field, vector Bin, pointing into the page. The parallel rails run from left to right, with one a distance ℓ above the other. The left ends of the rails are connected by a vertical wire containing a resistor R. The vertical bar lies across the rails to the right of the wire. The bar moves to the right with velocity vector v. (a) At what constant speed should the bar move to produce an 8.60-mA current in the resistor? m/s(b) What is the direction of the induced current? clockwisecounterclockwise    into the pageout of the page (c) At what rate is energy delivered to the resistor? mW(d) Explain the origin of the energy being delivered to the resistor.

Question A5 Consider an infinitely large sheet lying in the zz-plane at the origin, the extent of the sheet in the x, and z direction is infinite. The sheet carries surface current J = Jok, where Jo is the current per unit width perpendicular to the flow. Calculate the magnetic field everywhere (y > 0 and y < 0) due to J. Sketch the Amperian loop.

A metal rod of mass m slides without friction along two parallel horizontal rails, separated by a distance e and connected by a resistor R, as shown in the figure below. A uniform vertical magnetic field of magnitude B is applied perpendicular to the plane of the paper. The applied force shown in the figure acts only for a moment, to give the rod a speed v. In terms of m, e, R, B, and v, find the distance the rod will then slide as it coasts to a stop. d = R Fapp