a student uses a bar magnet of 0.1 mT to pick up paper clips. she is then instru

Question

a student uses a bar magnet of 0.1 mT to pick up paper clips. she is then instructed to design an electromagnet to pick up the paper clips. to do so she first has to design the electromagnet by doing the appropriate calculations. so design an electromagnet that will have the same magnetic field as the bar magnet. assume that the resistance is 3 ohms, diameter 0.2 mm and resistivity 1.7×10^-8 ohm-meter. what current will flow in the electromagnet? what is the length L of the wire needed and how many turns does it have? how long is the solenoid?
note: r of solenoid = 10 cm.

Explanation / Answer

resistance = resistivity * length / area

3 = 1.7 * 10^-8 * length / pi * (0.1 * 10^-3)^2

length of wire = 5.54399 m

given,

radius of the solenoid = 10 cm or 0.1 m

circumference = 2 * pi * r

circumference = 2 * pi * 0.1

number of turns = length / circumference

number of turns = 5.54399 / 2 * pi * 0.1

number of turns = 8.9 or approx 9 turns

length of solenoid = diameter of wire * number of turns

length of solenoid = 0.2 * 9

length of solenoid = 1.8 mm

magnetic field = k * N * I / L

0.1 * 10^-3 = 4 * pi * 10^-7 * 9 * I / 1.8 * 10^-3

I = 0.0159155 A

Current in the electromagnet = 0.0159155 A

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