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    Force on a Conductor Calculator (F = BIl)

    GCSE PhysicsAQAEdexcelOCRHigher tier

    Find the force, magnetic flux density, current or length using F = B × I × l, for a wire at right angles to a magnetic field.

    Quick answer

    Force = magnetic flux density × current × length. Use tesla, amps and metres to get newtons. For example, a 15 cm wire carrying 4 A in a 0.25 T field feels 0.25 × 4 × 0.15 = 0.15 N.

    By Engr. Mehmood Kakar · Updated

    F = B × I × l
    Find:

    Simulation

    The motor effect

    A wire carrying current out of the screen sits in a magnetic field pointing from N to S. Change the field, the current and the length in the field: the force grows with each.

    0.2 T
    4 A
    0.25 m

    Fleming’s left-hand rule: First finger = Field (N to S), seCond finger = Current, thuMb = Motion (force). Reverse the current or the field and the force reverses.

    Put these numbers in the calculator above

    How to use F = BIl

    A wire carrying a current in a magnetic field feels a force. This is the motor effect. When the wire is at right angles to the field, the force is:

    force = magnetic flux density × current × length

    • F is force in newtons (N)
    • B is magnetic flux density in tesla (T)
    • I is current in amperes (A)
    • l is the length of wire inside the field in metres (m)

    A 15 cm (0.15 m) wire carrying 4 A in a 0.25 T field feels a force of 0.25 × 4 × 0.15 = 0.15 N.

    Only the length of wire actually inside the magnetic field counts. The direction of the force is given by Fleming's left-hand rule, and the force is zero if the wire runs parallel to the field. Electric motors and loudspeakers both work using this force.

    Common mistakes that cost marks

    1. Leaving length in centimetres. 15 cm is 0.15 m.
    2. Not converting mT. 200 mT is 0.2 T.
    3. Using the whole wire length. Only the part inside the field counts.
    4. Dividing by only one term when rearranging. B = F ÷ (I × l): divide by both.

    Practice questions

    Try each one on paper first, then reveal the worked answer.

    Q1A wire 15 cm long carries a current of 4.0 A at right angles to a 0.25 T magnetic field. Calculate the force on it.[3 marks]
    1. F = B × I × l
    2. Convert: l = 15 ÷ 100 = 0.15 m
    3. F = 0.25 × 4.0 × 0.15
    4. F = 0.15 N
    Q2A 0.10 m wire carrying 2.0 A feels a force of 0.060 N in a magnetic field. Calculate the magnetic flux density.[3 marks]
    1. Rearrange: B = F ÷ (I × l)
    2. I × l = 2.0 × 0.10 = 0.20
    3. B = 0.060 ÷ 0.20
    4. B = 0.30 T
    Q3A 5.0 cm wire in a 0.20 T field feels a force of 0.012 N. Calculate the current.[3 marks]
    1. Rearrange: I = F ÷ (B × l)
    2. Convert: l = 0.050 m; B × l = 0.20 × 0.050 = 0.010
    3. I = 0.012 ÷ 0.010
    4. I = 1.2 A

    Endless practice

    A new question every time, marked instantly. Work it out on paper, then type your answer.

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    Frequently asked questions

    What is the equation for the force on a current-carrying wire?

    Force = magnetic flux density × current × length (F = BIl), for a wire at right angles to the field. F is in N, B in tesla (T), I in A and l in m.

    What is the motor effect?

    A wire carrying a current in a magnetic field experiences a force. This is what makes electric motors turn.

    How do I find the direction of the force?

    Use Fleming’s left-hand rule: First finger for the field, seCond finger for current, thuMb for motion (force).

    Is F = BIl Higher tier?

    Yes. In AQA GCSE Physics and Combined Science, calculations with F = BIl are Higher tier.