Which of the following is equivalent to tesla ?

Question

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Correct — C, Newton per ampere meter. The tesla is the SI unit of magnetic flux density, and the fastest way to derive it is from the force on a current-carrying conductor in a magnetic field, F = BIL. Rearranged, B = F/(IL), so the unit of B is the newton divided by the product of an ampere and a metre — newton per ampere metre, N/(A·m). The same result comes out of the Lorentz force on a moving charge, F = qvB, since B = F/(qv) gives newtons divided by coulomb-metres-per-second, and a coulomb per second is an ampere, so it reduces to N/(A·m) again. In base units the tesla is kg·s⁻²·A⁻¹, and it is equally often written as one weber per square metre. There is a second, purely logical route to the answer that does not need any of that physics, and it is worth seeing because it is the kind of observation that saves a mark under time pressure: one coulomb is one ampere-second, so 'newton per coulomb' and 'newton per ampere-second' in options (a) and (d) are the very same unit written two ways. A well-set question has one correct option, so two options that are identical must both be wrong — which eliminates half the list at a stroke. What that shared unit actually measures is electric field strength, not magnetic flux density. Option (b), ampere per newton, is not a standard unit of anything.

Why the other options are wrong — (a) The unit of electric field strength, equivalently the volt per metre — it measures the force on a unit of charge at rest, not on a moving charge or a current. It is the most familiar 'newton per something' in electromagnetism, which is precisely why it is offered first.  (b) Not the unit of any standard physical quantity. It is the tesla's own combination turned upside down and stripped of the metre, so it looks like it belongs on the list without corresponding to anything measurable.  (d) Identical to option (a), because one ampere-second is one coulomb — so this too is the unit of electric field, not of magnetic flux density. Two options expressing the same unit is a strong signal that neither is the answer, and the missing factor in both is the metre.

Concept: Magnetic flux density B, sometimes loosely called magnetic field strength, is defined by the force a magnetic field exerts on moving charge. Two standard expressions define it: F = BIL for a straight conductor of length L carrying current I at right angles to the field, and F = qvB for a single charge q moving with velocity v. Either gives the tesla as newton per ampere metre. The unit was named after Nikola Tesla and adopted into the SI in 1960; the older CGS unit, the gauss, equals one ten-thousandth of a tesla, which tells you how large a tesla is. For scale, the Earth's own magnetic field at the surface is only about 25 to 65 microtesla, a small refrigerator magnet is of the order of a few millitesla, and a clinical magnetic resonance imaging scanner runs at 1.5 or 3 tesla — which is why the machine's field strength is quoted in teslas in hospital literature. Keep the companion quantities straight: magnetic flux is measured in webers, and one tesla is one weber per square metre; electric field is measured in newtons per coulomb, equivalently volts per metre.

State PCS 2024 Q149 — Science & Technology PYQ with Answer

State PCS 2024 Q149 — Science & Technology PYQ with Answer