# 25.2.2 Magnetic Flux Density

### 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 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

### 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 Step 3:            Calculate the force F from the balance reading

F = mg             where g = 9.81 N kg-1

F = (1.2 × 10-3) × 9.81

Step 4:            Substitute values into magnetic flux density equation  ### Author: Katie

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.
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