# 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.

Answer:

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.