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 5mT
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
Magnetic Flux Density from a Current Balance
- Recall that there is a force on a current-carrying conductor (eg. a wire) when it is placed inside an external magnetic field
- For example, between the poles of a large horseshoe magnet
- When the magnet is placed on a current balance such as a top-pan weighing scale, the flux density B of the magnetic field can be obtained
- Assuming the magnetic field of the magnetic if uniform, the length L of the wire is measured using a ruler
- The wire is placed between the poles of the magnet so the current I flowing through will be perpendicular to the magnetic flux density B of the magnets
- When there is no current in the wire, the magnet is placed on top and the top pan balance is zeroed
- When current I flows through the wire, an ammeter reads its value
- Using Fleming’s left-hand rule, the direction of the current compared to the direction of the magnetic field lines is considered so the wire experiences a force upwards
- The force is directly proportional to the amount of current
- According to Newton’s third law, there is an equal and opposite force on the magnets
- The magnets are therefore pushed downwards and a reading appears on the scale of the balance
- This force is given by:
F = mg
- Where:
- F = force of the magnets pushing down on the balance scale (N)
- m = mass indicated on the top-pan balance scale (kg)
- g = acceleration due to gravity = 9.81 m s-2
- The magnetic flux density B between the magnets is defined by the equation:
- Where:
- B = magnetic flux density (T)
- F = magnetic force on the wire/force of the magnets pushing down (N)
- I = current (A)
- L = length of the wire (m)
- The force can be obtained from the balance reading and used as the force F in the magnetic flux density equation
- Effectively, the system ‘weighs’ the force on the wire
Step 1: Write down the known quantities
Length, L = 4.5 cm = 4.5 × 10-2 m
Current in the wire, I = 8.7 A
Mass increase, m = 1.2 g = 1.2 × 10-3 kg
Step 2: Magnetic flux density on a current-carrying wire equation