Calculating Magnetic Fields – Learn

The strength of the magnetic field around a current-carrying conductor and a solenoid can be determined quantitatively.

• The equation used to calculate the strength of the field around a current-carrying conductor, gives us the magnitude of the field at some distance, , from the conductor.
• The equation used to calculate the strength of the field in a solenoid, gives us the magnitude of the field at a point inside of the solenoid. The field within the solenoid is uniform.

Current-carrying conductors

The magnitude of the field () at some distance, , from the current-carrying conductor is given by:

where:

= the strength of the magnetic field (in Tesla)

= the permeability of free space ()

= the current in the wire (in amps)

= the radius, or distance from the wire (in m)

Solenoids

The magnitude of the field ( ) within a solenoid is given by:

where:

= the strength of the magnetic field (in Tesla)

= the permeability of free space ( )

= the number of turns in the coil

= the current in the wire (in amps)

= the length of the solenoid (in m)

Example 1:

What is the strength of a magnetic field at a distance of 5cm from a wire carrying a current of 10A?

where:

=  ( )

Example 2:

What is the strength of a magnetic field in a 15cm solenoid that has 250 turns carrying a current of 20A?