# You have 100 m of fine copper

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, apencil, and a bag of long nails made from 99.8% pure iron (relativemagnetic permeability of 200) you need to make a magnet that wouldproduce a strong magnetic field.

A. What is the resistance of the 100 m of thegiven copper wire? Assume the resistivity of copper to be ρ = 1.68× 10 − 8 Ω ⋅ m.

B. Assuming that you will use all the wire,what will be electric current if you connect the wire to the powersupply?

C. Would you build a toroid? A solenoid? Asimple loop? Justify your choice.

D. For the chosen design of the magnet,describe how you would build it and estimate the magnetic fieldthat you can achieve with it.

A.we have to find the resistance of the 100 m of the givencopper wire.

Given that resistivity=1.68*10^-8 m

We have to consider the equation relating resistance andresistivity which is given below.

R=*L/A

Here R is the resistance,is the resistivity,L is the length of the wire and A is the crosssectional area of copper wire.

L=100 m A=*r^2=3.14*0.0005^2=7.85*10^-7m^2 (where r is the radius of copper wire,r=0.5 mm=0.0005 m)

Again consider the equation for resistance,R=*L/Asubstitute the values in the equationand we get

R=1.68*10^-8*100/7.85*10^-7=1.68*10^-8*1.2738*10^-6=2.14*10^-14

The resistance of the copper wire is 2.14*10^-14

B.we have to calculate the current by knowing the relationbetween current,voltage and resistance.

According to ohm’s law V=I*R

Given that V=12 V and R=2.14*10^-14

Therefor I=V/R=12/2.14*10^-14=5.61*10^-14 A

Value of electric current=5.61*10^-14 A

C.I would build a toroid because it produce a large magneticfield than a solenoid and a simple loop.we have to produce a strongmagnetic field,so toroid is the better option.The ring likestructure of toroid favours the toroid to produce strong magneticfield and also it has high inductance.

D.we have to make a ring like structure by winding the copperwire in a special way.This creates an effect on the magneticfield.When we provide a smaller area and the magnetic lines offorce acting intersect each other to make a strong magneticfield,The magnetic field depends on number of turns and we canassume that the range of magnetic field is about 10 to 100Tesla.

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