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प्रश्न
Define one tesla using the expression for the magnetic force acting on a particle of charge q moving with velocity \[\vec{v}\] in a magnetic field \[\vec{B}\] .
उत्तर
One tesla is the defined as the magnitude of magnetic field which produces a force of 1 newton when a charge of 1 coulomb moves perpendicularly in the region of the magnetic field at a velocity of 1 m/s.
\[F = \text{ qv } B\]
\[ \Rightarrow B = \frac{F}{\text{qv}}\]
\[ \Rightarrow 1 T = \frac{1 N}{\left( 1 C \right)\left( 1 \text{ m/s} \right)}\]
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संबंधित प्रश्न
(a) Write the expression for the magnetic force acting on a charged particle moving with velocity v in the presence of magnetic field B.
A circular coil of wire consisting of 100 turns, each of radius 8.0 cm carries a current of 0.40 A. What is the magnitude of the magnetic field B at the centre of the coil?
A straight horizontal wire of mass 10 mg and length 1.0 m carries a current of 2.0 A. What minimum magnetic field B should be applied in the region, so that the magnetic force on the wire may balance its weight?
Explain "Magnetic force never does any work on moving charges".
A very high magnetic field is applied to a stationary charge. Then the charge experiences ______.
For a circular coil of radius R and N turns carrying current I, the magnitude of the magnetic field at a point on its axis at a distance x from its centre is given by,
B = `(μ_0"IR"^2"N")/(2("x"^2 + "R"^2)^(3/2))`
(a) Show that this reduces to the familiar result for field at the centre of the coil.
(b) Consider two parallel co-axial circular coils of equal radius R, and number of turns N, carrying equal currents in the same direction, and separated by a distance R. Show that the field on the axis around the mid-point between the coils is uniform over a distance that is small as compared to R, and is given by, B = `0.72 (μ_0"NI")/"R"` approximately.
[Such an arrangement to produce a nearly uniform magnetic field over a small region is known as Helmholtz coils.]
The magnetic moment of a current I carrying circular coil of radius r and number of turns N varies as ______.
In the product
`overset(->)("F") = "q"(overset(->)(υ) xx overset(->)("B"))`
= `"q"overset(->)(υ) xx ("B"overset(^)("i") + "B" overset(^)("j") + "B"_0overset(^)("k"))`
For q = 1 and `overset(->)(υ) = 2overset(^)("i") + 4overset(^)("j") + 6overset(^)("k")` and
`overset(->)("F") = 4overset(^)("i") - 20overset(^)("j") + 12overset(^)("k")`
What will be the complete expression for `overset(->)("B")`?
