The magnetic field 41.0 cm away from along, straight wire carrying current 7.00A

Question

The magnetic field 41.0 cm away from along, straight wire carrying current 7.00A is 3.41 µT. (a) At what distance is it 0.200 µT?
1 cm
(b) At one instant, the two conductors in a long householdextension cord carry equal 7.00 A currentsin opposite directions. The two wires are 3.00 mm apart. Find themagnetic field 41.0 cm away from themiddle of the straight cord, in the plane of the two wires.
2 nT
(c) At what distance is it one tenth as large?
3 cm
(d) The center wire in a coaxial cable carries current 7.00 A in one direction, and the sheath around itcarries current 7.00 A in the oppositedirection. What magnetic field does the cable create at pointsoutside?
4 nT (a) At what distance is it 0.200 µT?
1 cm
(b) At one instant, the two conductors in a long householdextension cord carry equal 7.00 A currentsin opposite directions. The two wires are 3.00 mm apart. Find themagnetic field 41.0 cm away from themiddle of the straight cord, in the plane of the two wires.
2 nT
(c) At what distance is it one tenth as large?
3 cm
(d) The center wire in a coaxial cable carries current 7.00 A in one direction, and the sheath around itcarries current 7.00 A in the oppositedirection. What magnetic field does the cable create at pointsoutside?
4 nT

Explanation / Answer

(a) field strength is inversely prop to distanceso... .          distance 1 *field 1 = distance 2 * field 2 .          distance 1 *0.200 = 41.0 * 3.41   . distance 1=   699 cm . (b)   the distance for the two wires to the pointare   410mm +/- 3mm/2   =   408.5 mm and   411.5 mm . So the mag field from each conductor is    k I/ r     and .    total B field =   k I ( 1 /r1 + 1 / r2 ) =  2 x 10-7 * 7.00 * ( 1 / 0.4085   + 1 /0.4115) = .              = 6829 x 10-9 T =    6829 nT . (c)     same idea... .             total B field =   k I ( 1 /r1 + 1 / r2 ) .             682.9 x 10-9 = 2 x 10-7 * 7.00*( 1 / r1 + 1 / r2) .            0.487786   = 1 / r1   + 1/r2 . but   r1   and r2    areboth      d +/-   0.0015m    s0 .        0.487786   =    (r1 + r2 ) / r1 r2 .         0.487786 (d +0.0015) (d - 0.0015)   =   2d .        0.487786d2    -    1.09752 x10-6 = 2d .         d2   -     4.10016 d     -   0.00000225      = 0 .       d =     4.100 m   =   410 cm . (d)   coaxial cable:    B fieldis   zero . but   r1   and r2    areboth      d +/-   0.0015m    s0 .        0.487786   =    (r1 + r2 ) / r1 r2 .         0.487786 (d +0.0015) (d - 0.0015)   =   2d .        0.487786d2    -    1.09752 x10-6 = 2d .         d2   -     4.10016 d     -   0.00000225      = 0 .       d =     4.100 m   =   410 cm . (d)   coaxial cable:    B fieldis   zero

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