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Magnetic Force on Wire Calculator

Find force F = BIL when wire is perpendicular to magnetic field

Parameters

Tⓘ
Aⓘ
mⓘ
Show Trail

Controls

xⓘ

Calculated Values

Force on Wire:
0.60;N0.60;N

Examples

Lab wire in horseshoe magnet

B=0.4 T, I=5 A, L=0.3 m.

    Strong field

    MRI fringe field B=1.5 T, I=2 A, L=0.1 m.

      Visualization

      Magnetic Force on Current-Carrying Wire

      A straight conductor of length L carrying current I in an external magnetic field B experiences a distributed magnetic force. Integrating over the wire gives the total force F⃗ = I L⃗ × B⃗ for a uniform field and straight segment. When the wire is perpendicular to B (θ = 90°), magnitude simplifies to F = BIL — one of the most used formulas in electromagnetism labs.

      The direction follows the right-hand rule: point fingers along the current I, curl them toward B; your thumb indicates the force on the wire. Reversing current or flipping B reverses F. When the wire is parallel to B, sin θ = 0 and the force vanishes — no push on a wire running along field lines.

      Microscopically, the force on the wire is the sum of Lorentz forces on drifting electrons (and positive ion background). Drift velocity v_d gives F/L = I(B × v̂_d) per unit length, which integrates to BIL for perpendicular geometry.

      Parallel current-carrying wires exert forces on each other: parallel currents (same direction) attract; anti-parallel repel. The force per unit length is F/L = μ₀I₁I₂/(2πd) where d is separation. This underlies the SI definition of the ampere.

      Practical example: B = 0.4 T, I = 5 A, L = 0.3 m gives F = 0.6 N — about the weight of 60 g. Loudspeakers and DC motors use many such segments in a coil to produce large net forces and torques τ = NIAB sin θ.

      Class 12 problems link straight-wire force to galvanometers, force balances, and rail-gun concepts. Always distinguish force on wire (external B) from field produced by the wire itself (Ampère's law).

      Key Concepts

      • F⃗ = I L⃗ × B⃗
      • F = BIL (wire ⊥ B)
      • RHR: I → curl B → thumb F
      • Parallel wires: same I attract
      • F = 0 when wire ∥ B

      Real-World Applications

      • DC motors and loudspeakers
      • Magnetic force balances (lab)
      • Parallel-wire ampere definition
      • Maglev and rail guns (concept)
      • Class 12 force-on-conductor numericals

      Explore Further

      More magnetism tools

      Physics Equations

      Force:
      F=BILF = BIL

      Step-by-Step Solution

      See how the main results are calculated.

      1

      Step 1: Force on Conductor

      Equation:

      F⃗=I L⃗×B⃗\vec{F} = I\,\vec{L} \times \vec{B}

      Explanation:

      Each current element IL feels a magnetic force in external field B.

      2

      Step 2: Straight Wire (θ = 90°)

      Equation:

      F=BILsin⁡θ=BILF = BIL\sin\theta = BIL

      Explanation:

      Wire perpendicular to B gives maximum force.

      3

      Step 3: List Given Quantities

      Result:

      B=0.4 T,I=5 A,L=0.3 mB = 0.4\ \text{T},\quad I = 5\ \text{A},\quad L = 0.3\ \text{m}
      4

      Step 4: Multiply

      Calculation:

      F=0.4×5×0.3=0.600000 NF = 0.4 \times 5 \times 0.3 = 0.600000\ \text{N}

      Result:

      F=0.600000NF = 0.600000 N
      5

      Step 5: Direction

      RHR: fingers along I, curl toward B, thumb = force on wire.

      Explanation:

      If wire ∥ B, then F = 0.

      6

      Step 6: Connection to Motors

      Equation:

      F=BIL ⇒ τ=NIABsin⁡θF = BIL\ \Rightarrow\ \tau = NIAB\sin\theta

      Explanation:

      Force on coil sides produces rotation in motors and galvanometers.

      Frequently Asked Questions (FAQ)

      Curved or bent wire?

      Use dF⃗ = I dL⃗ × B⃗ and integrate along the path. For uniform B and semicircle, geometry factors appear in the integral.

      Does the wire's own field matter?

      F = BIL uses external B only. The field from the wire itself does not exert a net force on the same wire.

      Why do parallel currents attract?

      Each wire creates B at the other; the Lorentz force on the second wire points toward the first when currents are parallel.

      AC current in B?

      Use instantaneous I(t); force oscillates at twice the frequency if B is constant and I is sinusoidal.

      Practice MCQs

      1. Force on wire (I ⊥ B):
      2. Doubling current doubles:
      3. Wire parallel to B:
      4. Same-direction parallel currents:
      5. Motor converts:
      6. F units:

      Related Calculators

      These tools connect to the same physics concepts used in this calculator.

      Lorentz ForceFind magnetic force on a moving charge: F = |q|vB.Ampere's Law — Straight WireMagnetic field B = μ₀I/(2πr) around a long wire.Solenoid FieldUniform field inside ideal solenoid: B = μ₀nI.Magnetic FluxFlux through a surface: Φ = BA cos θ.Ohm's LawCalculate voltage, current, and resistance in electrical circuits.Related Electricity topic.Error PropagationCombine measurement uncertainties for sums, products, quotients, and powers in experimental formulas.Related Measurement & Uncertainty topic.Quantum Harmonic OscillatorCalculate energy levels, wavefunctions, and quantum properties of harmonic oscillators.Related Modern Physics topic.Faraday's InductionInduced EMF from changing flux: |ε| = N|ΔΦ/Δt|.Part of the Class 12 — Magnetism learning path.