You are performing studies of the possibility of migrating birds using the Earth's magnetic field for navigation. To modify the magnetic field in the brain of a bird, you fit the bird with coils as "caps" and "collars" as shown in the figure below.
The illustration shows a bird with a long neck floating in water with metal coils fitted around its head and neck. The "cap" coil rests on top of its head like a crown. An identical second coil, the "collar" coil, encircles its neck just below its head. The planes of each coil are parallel to each other and to the surface of the water. A small button battery is secured on top of the bird's back. A wire running along the back of the bird's head connects the "cap" coil, the "collar" coil, and the battery.
The data on the coils indicate that they each have 210 Ω of resistance, a radius of 1.15 cm, and 50 turns of wire. The centers of the coils are separated by 2.25 cm. You wish to create an "Earth-like" magnetic field of 5.0 ✕ 10−5 T at the midpoint of the axis between the coils. Given this data, you need to determine the voltage of the battery (in V) needed to power the coils.
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