Magnetic Flux Density Definition
- The magnetic flux density B is defined as:
The force acting per unit current per unit length on a current-carrying conductor placed perpendicular to the magnetic field
- Rearranging the equation for magnetic force on a wire, the magnetic flux density is defined by the equation:
- Note: this equation is only relevant when the B field is perpendicular to the current
- Magnetic flux density is measured in units of tesla, which is defined as:
A straight conductor carrying a current of 1A normal to a magnetic field of flux density of 1 T with force per unit length of the conductor of 1 N m-1
- To put this into perspective, the Earth's magnetic flux density is around 0.032 mT and an ordinary fridge magnet is around 5 mT
Worked example
A 15 cm length of wire is placed vertically and at right angles to a magnetic field. When a current of 3.0 A flows in the wire vertically upwards, a force of 0.04 N acts on it to the left. Determine the flux density of the field and its direction.
Step 1: Write out the known quantities
Force on wire, F = 0.04 N
Current, I = 3.0 A
Length of wire = 15 cm = 15 × 10-2 m
Step 2: Magnetic flux density B equation
Step 3: Substitute in values
Step 4: Determine the direction of the B field
Using Fleming’s left-hand rule :
F = to the left
I = vertically upwards
therefore, B = into the page
