What is base SI unit of magnetic field

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The base SI unit of magnetic field (magnetic flux density) is the Tesla (T). To express it in terms of base SI units, we can use the formula for the magnetic force on a current-carrying wire.

  1. Recall the formula for the magnetic force (FF) on a current-carrying wire of length (LL) in a magnetic field (BB)

    F=BILF = BIL

    where II is the current.

  2. Rearrange the formula to solve for the magnetic field (BB)

    B=FILB = \frac{F}{IL}

  3. Substitute the SI units for each quantity

    • Force (FF): Newton (N)
    • Current (II): Ampere (A)
    • Length (LL): meter (m) So, the unit of BB is NA⋅m\frac{\text{N}}{\text{A} \cdot \text{m}}.

  4. Express the Newton (N) in terms of base SI units.

    From Newton's second law (F=maF=ma), we know that:

    1 N=1 kg⋅m⋅s−21 \, \text{N} = 1 \, \text{kg} \cdot \text{m} \cdot \text{s}^{-2}

  5. Substitute the base units for Newton into the expression for the magnetic field unit

    1 T=1 kg⋅m⋅s−21 A⋅m1 \, \text{T} = \frac{1 \, \text{kg} \cdot \text{m} \cdot \text{s}^{-2}}{1 \, \text{A} \cdot \text{m}}

  6. Simplify the expression by canceling out the meter (m) unit

    1 T=1 kg⋅A−1⋅s−21 \, \text{T} = 1 \, \text{kg} \cdot \text{A}^{-1} \cdot \text{s}^{-2}

    Therefore, the base SI unit of magnetic field (Tesla) expressed in terms of base physical quantities is:

    1 T=1 kg⋅A−1⋅s−2\boxed{\text{1 T} = \text{1 kg} \cdot \text{A}^{-1} \cdot \text{s}^{-2}}
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