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\fFigure (a) shows an element of length ds = 1.07 um in a very long straight wire carrying current. The current in that element sets up a differential magnetic field d B at points in the surrounding space. Figure (b) gives the magnitude dB of the field for points 5.1 cm from the element, as a function of angle 0 between the wire and a straight line to the point. The vertical scale is set by dB, = 62.4 pT. What is the magnitude of the magnetic field set up by the entire wire at perpendicular distance 5.1 cm from the wire? ds- Wire (a) dB, dB (pT) 0 1/2 0 (rad) (b) Number 5.65E-4 Units Tom VA straight conductor carrying a current i = 6.3 A splits into identical semicircular arcs as shown in the figure. What is the magnetic field at the center C of the resulting circular loop, which has a radius of 2.7 cm? Number i 2.15E-5 Units TThis answer has no units (degrees) m KE 5 m/5 m/5*2 N W N/m kg.m/s or N-5 N/m^2 or Pa kg/m* 3 E m/5*3 timesIn the figure, two concentric circular loops of wire carrying current in the same direction lie in the same plane. Loop 1 has radius 1.70 cm and carries 4.00 mA. Loop 2 has radius 2.80 cm and carries 5.70 mA. Loop 2 is to be rotated about a diameter while the net magnetic field B set up by the two loops at their common center is measured. Through what angle must loop 2 be rotated so that the magnitude of the net field is 95.0 nT? Number i 95.0 Units v\fA current is set up in a wire loop consisting of a semicircle of radius 4.04 cm, a smaller concentric semicircle, and two radial straight lengths, all in the same plane. Figure (a) shows the arrangement but is not drawn to scale. The magnitude of the magnetic field produced at the center of curvature is 47.34 //T. The smaller semicircle is then flipped over (rotated) until the loop is again entirely in the same plane (Figure (b)). The magnetic field produced at the (same) center of curvature now has magnitude 15.80 //T, and its direction is reversed. What is the radius of the smaller semicircle? (a) (b) Number 140 Unitsrad h km/h cm/s km/s E m* 3 KW kPa MPa KN m*3/s E/cm* 3 ME HE MW kg/s cm/s* 2 ft/s*2In Figure in}, wire 1 consists of a circular arc and two radial lengths; it carries current i1 = 0.690 A in the direction indicated. Wire 2, shown in cross section, is long, straight, and perpendicular to the plane of the gure. Its distance from the center of the arc is equal to a the radius R of the arc. and it carries a current i2 that can be varied. The two currents set up a net magnetic eld B at the center of the arc. Figure (bl gives the square of the eld's magnitude 32 plotted versus the square of the current 22. The vertical scale is set by 352 = 11.9 x 10'10 T2. What angle is subtended bythe arc? (E?) (a) Number n 15.8 Units V Three long wires all lie in an xy plane parallel to the x axis. They intersect the y axis at the origin, y = d, and y = 2d, where d = 13 cm. The two outer wires each carry a current of 3.8 A in the positive x direction. What is the magnitude of the force on a 1.7 m section of either of the outer wires if the current in the center wire is 3.6 A (a) in the positive x direction and (b) in the negative x direction? (a) Number i 5.47E-4 Units N (b) Number 16.9E-6 Units N