Question

Which of the following graph represent the variation of magnetic flux density B with distance r for a straight long wire carrying an electric current?​

Answer 1

we have to identify the graph which represents the variation of manetic flux density B with distance r for a straight long wire carrying an electric current I.

solution : the magnetic flux density or magnetic field intensity with distance r  for a straight long wire carrying an electric current I is given by,

                                   B = $\frac{\mu_0I}{2\pi r}$

where $\mu_0$ is permeability of vacuum.

here it is clear that magnetic flux density is inversely proportional to seperation of wir to the point of observation.

i.e., B ∝ 1/r

hence the graph would be hyperbolically decreasing. which is shown in the figure.

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Answer 2

Graph of Magnetic Flux Density vs Distance:

• We will first calculate the magnetic flux density of the infinite wire using AMPERE-CIRCUITAL LAW.

• We will consider a circular closed path around the wire at distance r from wire.

$\therefore \displaystyle \oint B \times dl = \mu_{0}(i)$

$\implies \displaystyle B \oint dl = \mu_{0}(i)$

$\implies \displaystyle B (2\pi r) = \mu_{0}(i)$

$\implies \displaystyle B = \dfrac{\mu_{0}(i) }{2\pi r}$

$\boxed{ \implies \displaystyle B \propto \dfrac{1 }{r}}$

• We will get a HYPERBOLIC CURVE if we plot B vs r graph.

So, OPTION C) IS CORRECT ✔️