In studies of the possibility of migrating birds using the Earth\'s magnetic fie

Question

In studies of the possibility of migrating birds using the Earth's magnetic field for navigation, birds have been fitted with coils as "caps" and "collars" as shown in the figure below. (a) If the identical coils have radii of 1.12 cm and are 2.41 cm apart, with 57 turns of wire apiece, what current should they both carry to produce a magnetic field of 4.40 10-5 T halfway between them? mA (b) If the resistance of each coil is 250 , what voltage should the battery supplying each coil have? V (c) What power is delivered to each coil? mW explain what you did and why please

Explanation / Answer

the magnetic field B along th symmetry of the loop

B = uo I r^2 /(2(x^2 r^2)^3/2

here x = d/2 for 2N loops

so B = uo I r^2/(2 (d^2/4 + r^2)^3/2

Currrent I = (B/uo r^2) * (2 (d^2/4 + r^2)^3/2/2N

I = B *(d^2/4 + r^2)^3/2 /(uo r^2 N)

I = (4.4*10^-5) * (0.0241^2/4 + 0.012^2)^3/2/(4*3.14 *10^-7 * 0.012^2* 57)

I = 10.4 mA

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part B . ohms law V = iR

V = IR = 10.4 e -3 *250

V = 2.6 V

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c.

The power delivered to each coil is P = VI

P = 10.4 e-3 * 2.6

P = 27.04 mW

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