Two long fixed parallel wires, A and B , are 10cm apart in air and carry 40 A an

Question

Two long fixed parallel wires, A and B, are 10cm apart in air and carry 40 A and 20 A respectively, in oppositedirections. Determine the resultant field (a) on a line midwaybetween the wires and parallel to them and (b) on a line 8.0 cmfrom wire A and 18 cm from wire B (c) What is theforce per meter on a third long wire, midway between A andB and in their plane, when it carries a current of 5.0 Ain the same direction as the current in A.

1) (a) 8.0 x 10-5 T (b) 1.2 x 10-4 T (c)1.2 x 10-3 N/m, toward B

2) (a) 2.4 x 10-4 T (b) 7.8 x 10-5 T (c)1.2 x 10-3 N/m, toward A

3) (a) 2.4 x 10-6 T (b) 7.8 x 10-7 T (c)0

4) (a) 1.2 x 10-4 T (b) 5.6 x 10-6 T (c)2.1 x 104 N/m, toward A

Explanation / Answer

You have to calculate the B field from each wire and add orsubtract them appropriately. When the point is between the wires,the B fields add. When the point is on the same side of bothwires, the B fields subtract. . (a) Each B field is given by     k I/ r       where k = 2 x 10-7 . So... B field from A = 2 x 10-7 *40 / 0.05 =   1.60 x 10-4 .                    from B = 2 x 10-7 * 20 / 0.05 =   0.80 x 10-4 .    Total B field =    2.40 x10-4   Tesla . (b)   B field from A = 2 x10-7 * 40 / 0.08 =   1.00 x10-4 .                    from B = 2 x 10-7 * 20 / 0.18 =   0.222 x 10-4 .    Total B field =    7.8 x10-5   Tesla . (c) Force per meter = B field *current = 2.40 x 10-4 * 5 =    1.20 x10-3    Newtons   towardA. . CORRECT ANSWER IS #2 .    Total B field =    2.40 x10-4   Tesla . (b)   B field from A = 2 x10-7 * 40 / 0.08 =   1.00 x10-4 .                    from B = 2 x 10-7 * 20 / 0.18 =   0.222 x 10-4 .    Total B field =    7.8 x10-5   Tesla . (c) Force per meter = B field *current = 2.40 x 10-4 * 5 =    1.20 x10-3    Newtons   towardA. . CORRECT ANSWER IS #2 .                    from B = 2 x 10-7 * 20 / 0.18 =   0.222 x 10-4 .    Total B field =    7.8 x10-5   Tesla . (c) Force per meter = B field *current = 2.40 x 10-4 * 5 =    1.20 x10-3    Newtons   towardA. . . CORRECT ANSWER IS #2

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