3. Wire and Circular Loop Consider a very long straight wire that lies on the m-axis. The wire carries current. 11 in the +at-direction. The magnetic eld due to the wire at any point in the qty-plane is -' tinI1 B: Tags; A circular loop of wire has a radius R and lies in the qty-plane with its center at (0 2R 0). It carries a counterc:lockwise current I2 (viewed from a point on the +z-axis). We want to nd the net magnetic force on the loop due to the straight wire using F: I I2 d? x B (a) (b) _). _, Find an expressmn for (if, an inmtesnnal d1splacement around the clrcular loop 111 the direction of the current, in terms of R, 6', d9, and unit vectors i,j, k, as needed. The angle 8 is dened in the gure above. Consider the direction of the force on an innitesimal segment, df' = I2 affix B Based on the properties of the cross~product and symmetry, identify which two of the three Cartesian components of B have to be zero and explain the reasoning behind this conclusion carefully. What is the expression for (If which may show the angle (19) dependence? Now set up your integral B : I" I2 (fix B, simplifying the integrand as much as possible. Be sure to write the limits on the integral. Perform the integration: what is the net magnetic force on the loop? Feel free to use Wolfram Alpha or another such tool to help perform the integration. Imagine that the ring with the current I2 is moving toward or away from the innite wire with the current 11 because of the magnetic force you found in part (c). The kinetic energy should increase with time. Does this mean that the energy conservation law is violated? If not, where does this increase in kinetic energy come from? This is more like a conceptual question with open discussion, so you don't have to derive the kinetic energy