Question

Question 2 14 pts You have 100 m of fine copper wire with a radius of 0.5 mm. Having only a 12 V power supply that can be treated as ideal, a pencil, and a bag of long nails made from 99.8% pure iron (relative magnetic permeability of 200) you need to make a magnet that would produce a strong magnetic field. A. (2 points) What is the resistance of the 100 m of the given copper wire? Assume the resistivity of copper to be p= 1.68 x 10-8 12. m. B. (2 points) Assuming that you will use all the wire, what will be electric current if you connect the wire to the power supply? C. (4 points) Would you build a toroid? A solenoid? A simple loop? Justify your choice. D. (6 points) For the chosen design of the magnet, describe how you would build it and estimate the magnetic field that you can achieve with it.

Answer 1

A)

R = pL / A

where p is resistivity

R = 1.68e-8 * 100 / pi * 0.5e-32

R = 2.14 ohms

____________________________

B)

V = IR

I = V / R

I = 12 / 2.14

I = 5.6 A

_____________

C)

I will build a solenoid because with the given materials, a uniform, strong field can be established

___________

D)

Wrap the given 100 m wire into muliple circular loop arranged closely in a series. Any current passing through these loops will produce a uniform magnetic field. Now To make magnetic field more strong, we will add the iron nails into the coils. Just assume as if we have wrapped the fine wire on an iron nail in a circular mannner.

B = kNI / L

where k is permeability of core, for iron k = 6.3e-3 and N is number of turns which you give, I is current found in part B and L is length of solenoid ( not wire)