# 7.8.3 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: • Where:
• B = magnetic flux density (T)
• F = magnetic force (N)
• I = current (A)
• L = length of the wire (m)
• 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 wire 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
• The magnetic flux density is sometimes referred to as the magnetic field strength

#### Worked Example

A 15 cm length of wire is placed vertically and at right angels 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, L = 15 cm = 15 × 10-2 m

Step 2: Write out the 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

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