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Question

Which of the following is equivalent to tesla ?

This question was previously asked in
BPSC 70th 2024 Prelims General Studies Question Paper (13-Dec-2024)
The correct answer is

Newton per ampere meter

One tesla is one newton per ampere metre — option 4.

Derive it from the force law. The force on a straight conductor of length L carrying a current I in a magnetic field B, at right angles to it, is

\(F=BIL\)

Rearranging for the field :

\(B=\dfrac{F}{IL}\qquad\Rightarrow\qquad1\ \text{T}=1\ \dfrac{\text{N}}{\text{A}\cdot\text{m}}\)

So the tesla is defined as the field which exerts a force of one newton on a conductor of one metre carrying one ampere.

OptionWhat it is
Ampere per newtonThe reciprocal of a force per current — no standard quantity
Newton per coulombElectric field strength, equal to volt per metre — a different quantity altogether
Newton per ampere-secondAmpere-second is a coulomb, so this is again N/C, electric field
Newton per ampere metre✓ Magnetic flux density, the tesla

Notice that options 2 and 3 are the same thing written two ways, since one coulomb is one ampere-second. Two identical options cannot both be the answer, so both can be rejected at once — a useful piece of examination logic.

Other equivalent forms. Since one weber is one tesla times one square metre :

\(1\ \text{T}=1\ \dfrac{\text{Wb}}{\text{m}^{2}}=1\ \dfrac{\text{kg}}{\text{A}\cdot\text{s}^{2}}=1\ \dfrac{\text{V}\cdot\text{s}}{\text{m}^{2}}\)

A sense of scale. The tesla is a very large unit. The Earth’s magnetic field is only about 25 to 65 microtesla; a refrigerator magnet is around 5 millitesla; a hospital MRI scanner works at 1·5 to 3 tesla. The older CGS unit, the gauss, is one ten-thousandth of a tesla, which is why the Earth’s field is often quoted as about half a gauss. The unit is named after Nikola Tesla.

Hence, the answer is newton per ampere meter.

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