Question

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. What is the resistance of the 100 m of the given 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 power supply?

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

D. 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.we have to find the resistance of the 100 m of the given copper wire.

Given that resistivity=1.68*10^-8 m

We have to consider the equation relating resistance and resistivity 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 cross sectional area of copper wire.

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

Again consider the equation for resistance,R=*L/A substitute 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 relation between 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 magnetic field than a solenoid and a simple loop.we have to produce a strong magnetic field,so toroid is the better option.The ring like structure of toroid favours the toroid to produce strong magnetic field and also it has high inductance.

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