Question:

A wire bent into a semicircle of radius R forms a closed circuit and carries a current I. The Wire lies in the xy plane, and a uniform magnetic field is directed along the positive y axis as in Figure 29.20. Find the magnitude and direction of the magnetic force acting on the straight portion 3' E of the wire and on the curved portion assuming 0.877 A current, 0.35 T '5' r1? magnetic field and 9 = 33 and R = 24 cm. Show the integration step by step R r159 and then solve numerically. ' A A wire bent into a semicircle of radius R forms a closed circuit and carries a current I. The wire lies in the xy plane, and a uniform magnetic field is directed along the positive yaxis as in the figure. Find the magnitude and direction of the magnetic force acting on the straight portion of the wire and on the curved portion. \fNo magnetic forces act on B sides O and 3 because these sides are parallel to B. A F, =FA =laB 1 R d s 2 4 de b 3 NO max =F2 -+FA X 2 Sides 2 and 4 are b perpendicular to the magnetic field and experience forces. =(laB + (laB a 2 The magnetic forces Fo and F4 = labB exerted on sides 2 and 4 create a torque that tends to rotate the loop clockwise. = LAB O 4 O FAYb b T = F - sin O+ F - sin 0 2 2 b 2 O A = laB - sin 8 + laB - sin O = labB sin O B 2 N O sin 0 = LAB sin 0 4 Fo When the normal to the loop makes an angle 0 with the 4 magnetic field, the moment arm O B for the torque is (b/2) sin 0.,2: (2) Your thumb points in the_, . direction of A (1) Curl your . . and [1,. fingers in the direction of the current around the 1001'). K \\|_.V 1