Magnetic flux density B and definition of the tesla.

The idea

Magnetic flux density B measures the strength of a magnetic field in terms of the force it exerts on a current. It is a vector quantity, with the direction of B along the field line from north to south. The tesla is defined from F = BIl when the conductor is perpendicular to the field: one tesla is the magnetic flux density producing a force of one newton on a straight conductor of length one metre carrying a current of one ampere perpendicular to the field. The unit T is equivalent to N A⁻¹ m⁻¹. The magnitude of the force is F = BIl sin θ, where θ is the angle between the conductor and the field. B is distinguished from magnetic flux Φ, measured in webers, where Φ = BA for a uniform field perpendicular to area A.

What earns the marks

• Defines magnetic flux density as the force per unit current per unit length on a conductor perpendicular to the field.
• States that the tesla is the unit of magnetic flux density and is equivalent to N A⁻¹ m⁻¹.
• Uses F = BIl for a conductor perpendicular to a uniform magnetic field and rearranges it to find B, F, I or l.
• Explains that the force is maximum when the conductor is perpendicular to B and zero when parallel, using F = BIl sin θ.
• Describes B as a vector whose direction is the direction of the magnetic field from north to south.
• Distinguishes magnetic flux density B from magnetic flux Φ, including the relationship Φ = BA for a uniform perpendicular field.

Common mistakes and how to put them right

• Confusing magnetic flux density B with magnetic flux Φ.

  Put it right: B is force per unit current per unit length, while Φ is the total field passing through an area, so use Φ = BA to link them.

• Using F = BIl when the conductor is not perpendicular to the field.

  Put it right: Include sin θ, where θ is the angle between the conductor and the field, so the magnitude of the force is BIl sin θ.

• Writing the unit as N A m⁻¹ without the inverse on the ampere.

  Put it right: The correct equivalent unit is N A⁻¹ m⁻¹, because current is divided by in the definition.

Exam tips

• When defining the tesla, specify one newton, one ampere, one metre and perpendicular orientation, because each condition is part of the definition.
• Show the rearrangement of F = BIl before substituting values so that the examiner can follow your method.
• If a question gives an angle, check whether it is measured between the conductor and the field or between the conductor and the normal to the field, and use sin θ only for the angle between conductor and field.