21 Physics Fall 2007
Solution to HW-14
A Wire and a Compass You are looking straight down on a magnetic compass lying flat on a table. A wire is stretched horizontally under the table, parallel to and a short distance below the compass needle. The wire is then connected to a battery so that a current I flows through the wire. This current causes the north pole of the compass needle to deflect to the left. The following questions ask you to compare the effects of different actions on this initial deflection. (A) If the wire is lowered farther from the compass, how does the new angle of deflection of the north pole of the com-pass needle compare to its initial deflection? IT IS SMALLER because the magnitude of the B field decreases when the wire is moved further away. (B) With the wire back at its initial location, you connect a second identical battery in series with the first one. When you close the switch, how does the new angle of deflection of the north pole of the compass needle compare to its initial deflection? IT IS LARGER because the increased current due to the second battery causes a stronger B field. Magnetic Field Generated by a Finite, Current-Carrying Wire A steady current I is flowing through a straight wire of finite length. (A) Find B_1, the magnitude of the magnetic field generated by this wire at a point P located a distance x from the center of the wire. Assume that at P the angle subtended from the midpoint of the wire to each end is as shown the in diagram. (B) Now find B_2, the magnetic field generated by this wire at a point P located a distance x from either end of the wire. Assume that at P the angle subtended from the end of the wire to the other end is as shown in the diagram
Force between a Long Wire and a Square Loop (modified) A square loop of wire with side length a carries a current I_1. The center of the loop is located a distance d from an infinite wire carrying a current I_2. The infinite wire and loop are in the same plane; two sides of the square loop are parallel to the wire and two are perpendicular as shown. (A) What is the magnitude F of the net force on the loop? (B) Write F in terms of =I A , the area of the loop times the current. ( is the magnetic moment.)
Canceling a Magnetic Field (modified) Four very long, currentcarrying wires in the same plane intersect to form a square with side lengths of 45.0 cm, as shown in the figure. The currents in the wires are 8.0 A, 20.0 A, 10.0A, and I. (A) Find the MAGNITUDE of the current I that will make the magnetic field at the center of the square equal to zero. (B) What is the direction of the current I?
28-36 The figure shows, in cross section, several conductors that carry currents through the plane of the figure. The currents have the magnitudes I_1 = 3.5 A, I_2 = 6.4 A, and I_3 = 1.6 A, and the directions shown. What are the line integrals of B . dl for the paths labelled a, b, c, and d? (go counterclockwise for all paths)