Question

A wire bent into the shape of a semicircle of radius Rforms a closed circuit and carries a current I. The circuit lies in the xy plane, and a uniform magnetic field is present along the positive y axis as in Figure 29.12. Find the magnetic force on the straight portion of the wire and on the curved portion. Please answer the part I circled in red!!! Thank you!

2. 2.2/5 points | Previous Answers PSE6 29 AE 02 Example 29.2 Force on a Semicircular Conductor Problem A wire bent into the shape of a semicircle of radius R forms a closed circuit and carries a current I. The circuit lies in thee xy plane, and a uniform magnetic field is present along the positive y axis as in Figure 29.12. Find the magnetic force on the straight portion of the wire and on the curved portion. Strategy Use Figure 29.12. Figure 29.12 The net magnetic force acting on a closed current loop ina uniform magnetic field is zero. In the setup shown here, the magnetic force on the straight portion of the loop is Fi and out of the screen, whereas the force on the curved portion is F2 and into the screen Solution e force on the straight portion of the wire has the following magnitude because L perpendicular to B. (Use the following as necessary: I, R, and B.) 2R and the wire is e direction of F1 is out of the paper because L × B is outward. (That is, L is to the right, in the direction of the current, and so by the rule of cross products, Lx B is outward.) To find the magnetic force on the curved part, we first write an expression for the magnetic force aF 2 on the element ds. If θ is the angle between B and as in Figure 29.12, the magnitude of dF2 is the following To integrate this expression, we express as in terms of θ. Because s-Ra, ds-Rde, and the expression for dF2 can be written as follows dF2-IRB sin θ de o obtain the total magnetic force F2 on the curved portion, we integrate this expression to account for contributions from all elements. Note that the direction of the magnetic force on every element is the same: into he paper (because dsx B is inward). Therefore, the resultant magnetic force F2 on the curved wire must also be into the paper. Integrating dF2 over the limits θ-0 to θ-π (i.e., the entire semicircle) gives the following (Use the following as necessary: I, R, and B.) F2=-1 RB (-1-1) Because the vector F2 is directed into the paper and because the force on the straight wire is directed out of the paper, we see that the magnitude of the net magnetic force on the closed loop is: (Use the following as necessary: I, R, and B.) Exercise 29.2 Hints: Getting Started I I'm Stuck Calculate the magnitude of the magnetic force per unit length exerted on a conductor carrying a current of 28.0 A in a region where a uniform magnetic field has a magnitude of 0.99 T and is directed perpendicular to the conductor. Fe 27.72 N/m

Answer 1