Consider the system pictured in the figure below. A ℓ = 12-cm length of conductor of mass 29 g, free to move vertically, is placed between two thin, vertical conductors, and a uniform magnetic field acts perpendicular to the page. When a 5.0-A current is directed as shown in the figure, the horizontal wire moves upward at constant velocity in the presence of gravity. Either end of a horizontal bar of length ℓ, shaped in a loop at each end, is threaded onto one of two thin, vertical, parallel conductors, forming an H shape. A current of 5.0 A flows counterclockwise through the bottom part of the H shape.

Two coplanar and concentric circular loops of wire carry currents of I, = 5.90 A and I, = 2.30 A in opposite directions as in the figure below. Let r, = 12.0 cm and r, = 8.60 cm. (Assume the positive direction along the axis perpendicular to the faces of the loops is out of the screen (towards you) and assume the positive vertical direction is toward the top of the screen.) (a) What is the magnitude of the net magnetic field (in µT) at the center of the two loops? PT (b) What is the direction of the net magnetic field at the center of the two loops? out of the screen O into the screen O toward the top of the screen O toward the bottom of the screen (c) Let r, remain fixed at 12.0 cm and let r, be a variable. Determine the value ofr, (in cm) such that the net field at the center of the loops is zero. cm

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.

A long, rectangular loop of width w, mass M, and resistance Ris at rest, with the plane of the loop parallel to the ground. Immediately to the left of the loop is a region of uniform magnetic field B that points into the screen. At time í = 0, a constant force F pushes the loop to the left, into the magnetic field region, as shown in the figure. Derive an expression for the speed v of the loop immediately after it enters the magnetic field region in terms of the given variables and the time t. U =

In each of the figures below, a uniform magnetic field B points in the +x-direction. The magnitude of the field is 3.00 T. In each figure, a square loop, shown edge-on, with sides of length { = 0.380 m, is oriented within the magnetic field as shown. In the left figure, the loop is oriented vertically, perpendicular to the magnetic field. In the middle figure, it is tilted such that the plane of the loop makes a 60.0° angle with the magnetic field. In the right figure, the loop is oriented horizontally, parallel to the magnetic field. 60.0 What is the magnetic flux (in Wb) through the loop in each of the three cases shown? (a) perpendicular to the magnetic field Wb (b) 60.0° from the magnetic field Wb (c) parallel to the magnetic field Wb

A "double-loop" planar structure shown in the figure below is made out of a thin wire with the resistance per unit length 5-0.131 /m. The length parameter of the structure a-47.4 cm. The structure is in the region of the uniform magnetic field as shown, where the normal component of the field changes with time t as B(t)-B, cos(2xft), where amplitude 8-349.8 G and frequency f-74 Hz. B a 2a X X X X Xax Q With the harmonically varying magnetic field, the induced currents in various segments of the structure will also be changing periodically with the same frequency. Find magnitude Io of the variable induced current in segment PQ shown in the figure: Jo=