Chapter 29, Problem 057 A student makes a short electromagnet by winding 500 tur

Question

Chapter 29, Problem 057 A student makes a short electromagnet by winding 500 turns of wire around a wooden cylinder of diameter d 4.8 cm. The coil is connected to a battery producing a current of 5.5 A in the wire. (a) What isthe magnitude of the magnetic dipole moment of this device? b) At what axial distance z >> d will the magnetic field have the magnitude 5.1 ?? approximately one tenth that of Earth's magnetic field)? Units (a) Number (b) Number Click if you would like to Show Work for this question: Units Open Show Work Question Attempts: 0 of 5 used SAVE FOR LATER SUBMIT ANSWER SUBMIT ANSWER

Explanation / Answer

a) magnetic dipole moment = N I A = N I * (pi r2)

= 500 * 5.5 * (pi * (0.048/2)2)

= 4.98

b) B = BH / 10

5.1 * 10-6 = mu0 n I A / 2 pi x3

5.1 * 10-6 = (4 pi * 10-7 * 500 * 5.5 * (pi * (0.048/2)2)) / 2 pi x3

x3 = (4 pi * 10-7 * 500 * 5.5 * (pi * (0.048/2)2)) / (2 pi * 5.1 * 10-6)

x = 0.580 m = 58 cm

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