Question

2. A steady, uniform magnetic field B with unknown magnitude and direction exists throughR out the shaded rectangular region shown here (diagrams are not to scale). This region is planar-entirely in the r-y plane (+x is east and +y is north). The region's width (from its west edge to its east edge) is a known distance D. The region's length (from its north edge to its south edge) is 10D. Consider the following experiments, all performed with this field. Experiment i A single circular loop of wire of diameter D is given a net charge of +Q. distributed uniformly along the wire. The loop is then placed with its center located at the exact center of the field, as shown here (view of the loop is edge-on). Then the loop is made to spin-like a wheel-around a north-south axis through its center, at a known steady rate eo(given in rpm) with the tangential velocity vectors for its westernmost and easternmost paints as shown. Result: The total magnetic field at the loop's center is zero. Experiment ii: The loop's spinning is halted, and the loop is discharged; it's now a neutral wire. Then the wire is cut and re-shaped into a single straight length, and held randomly within the field (so that its entire length is in the rplane and completely within the field). A steady current I is then sent through it and the magnetic force acting on the wire is measured. Using that same current I, the wire is re-pasitioned various times (always holding it completely within the field) until the maximum possible magnetic force magnitude has been achieved. Call this value F Experiment (ii: Now the wire is rotated so that its current (still the steady / from experiment south. Then a second identical length of wire is fixed in place parallel to the first wire, at a distance D/S50 to the east of the first wire. This second wire carries three times as much current as the first wire, and its current also flows south. is flowing directly a. Find an expression for the total magnetic force (magnitude and direction) exerted on the first wire b. Find an expression for the total magnetic field magnitude at a point midway between the two wires. Your answers should be expressions that include only known values, and for full credit, you must show that the units of vur solutions are also correct. These values are known: D. Q, co F

Answer 1

Here we apply concept of magnetic field due to Current and force on current carrying wire.

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