At what distance from a wire carrying a $10\mathrm{A}$ current is the magnetic field strength equal to $50\mathrm{\mu }\mathrm{T}$? This is the approximate value of the Earth's magnetic field.

(II) Consider a straight section of wire of length d, as in Fig. 28–51, which carries a current I. (a) Show that the magnetic field at a point P a distance 𝑅 from the wire along its perpendicular bisector is

$B=\frac{{\mu }_{0}I}{2\pi R}\frac{d}{(d^2+4R^2{)}^{\frac{1}{2}}}$

(b) Show that this is consistent with Example 28–10 for an infinite wire.

(II) Two long parallel wires 8.20 cm apart carry 19.5-A dc currents in the same direction. Determine the magnetic field vector at a point P, 12.0 cm from one wire and 13.0 cm from the other. See Fig. 28–43. [Hint: Use the law of cosines. See Appendix A or inside rear cover.]

Determine the magnetic field at a point P due to a very long wire with a square bend as shown in Fig. 28–63. The point P is halfway between the two corners.

(II) Two long thin parallel wires 13.0 cm apart carry 25-A currents in the same direction. Determine the magnetic field vector at a point 10.0 cm from one wire and 6.0 cm from the other (Fig. 28–37). [Hint: You could try using the law of cosines, Appendix A.]

Currents in dc transmission lines can be 100 A or higher. Some people are concerned that the electromagnetic fields from such lines near their homes could pose health dangers. For a line that has current 150 A and a height of 8.0 m above the ground, what magnetic field does the line produce at ground level? Express your answer in teslas and as a percentage of the earth's magnetic field, which is 0.50 G. Is this value cause for worry?