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Problem statement:

A steady current I flows along an infinitely long hollow cylindrical conductor of radius $R$. This cylinder is placed coaxially inside an infinite solenoid of radius $2R$. The solenoid has $n$ turns per unit length and carries a steady current $I$. Consider a point $\text{P}$ at a distance $r$ from the common axis.

The correct statement(s) is (are):

  • (A) In the region $0 < r < R$, the magnetic field is non-zero

  • (B) In the region $R < r < 2R$, the magnetic field is along the common axis.

  • (C) In the region $R < r < 2R$, the magnetic field is tangential to the circle of radius r, centered on the axis.

  • (D) In the region $r > 2R$, the magnetic field is non-zero.

The given solution is that both (A) and (D) are correct statements. However, is there an alternate argument for (C) is also being correct since the magnetic field in the region $R < r < 2R$ is touches the circle of radius $r$ only at a single point and meets all the requirements of being a tangent?

A detailed argument can be found here:

Analysis of Option C

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closed as off-topic by Michael Seifert, John Duffield, tpg2114 May 11 at 7:16

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  • $\begingroup$ There is obviously only one solenoid, and no question asked... $\endgroup$ – TZDZ Dec 5 '14 at 9:18
  • $\begingroup$ Yeah I corrected it. It would be great if you could answer it too. $\endgroup$ – stochastic_zeitgeist Dec 5 '14 at 10:45
  • $\begingroup$ Sorry, what is the question exactly ? $\endgroup$ – TZDZ Dec 5 '14 at 10:52
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    $\begingroup$ well, in your reasoning, every vector is tangent to any circle... $\endgroup$ – TZDZ Dec 7 '14 at 10:48
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    $\begingroup$ I'm voting to close this question as off-topic because it's more about the definition of a tangent than about physics. $\endgroup$ – Michael Seifert May 10 at 12:42
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Tangent to any curve is defined as a line touching the curve at a single point and that lies in the plane of the curve. Hence only [A] vector is the tangential vector. A tangential vector indicates the slope and hence it must lie on the plane of the curve

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tangent is a secant where point A tends to point B please refer to the definition of tangent https://en.wikipedia.org/wiki/Tangent#Tangent_line_to_a_curve

hence answer ad looks correct

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