
where I is the current in amperes, r is the distance of the point from the wire in meters.
The constant
o is called the permeability of
free space. The universal value of the permeability of free space is 4
x 10-7 T m/A.
Example Problem:
What is the magnetic field at a distance of 2.00 m from a straight conducting wire that carries a current of 3.00 mA.
Solution:
B = 4
x 10-7 T m/A x 3.00 x 10-3
A/[2
x 2.00 m] = 3.00 x 10-10 T
Problems:
1. What is the current in a straight conducting wire that produces a magnetic field of 5.00 x 10-7 T at a distance of 10.0 cm from the wire?
2. A straight conducting wire allows 2.50 x 1018 electrons to pass a point in 5.00 s. What magnetic field would be produced 10.0 cm from the wire?
3. How far from a straight conducting wire that carries a current of 1.20 ma will the magnetic field intensity be 4.00 x 10-5 T?
The Magnetic Field of a Straight Wire
After completing this module:
1. You will recall the SI unit for magnetic field strength.
2. You will recall the formula for the magnetic field around a straight conductor carrying an electric current.
3. You will solve simple problems using the formula.
The magnetic field strength at any point in space may be measured using SI units. The convenience SI unit is the tesla [T], which reduces to its base unit form – kg/[A.s2].
The magnetic field strength at a point near a straight conducting wire is directly proportional to the current in the wire and inversely proportional to the distance of the point from the wire. The field, B may be expressed thus: