Find magnetic field in a solenoid for different regions? [closed]

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

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "Homework-like questions should ask about a specific physics concept and show some effort to work through the problem. We want our questions to be useful to the broader community, and to future users. See our meta site for more guidance on how to edit your question to make it better" – tpg2114
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• There is obviously only one solenoid, and no question asked... – TZDZ Dec 5 '14 at 9:18
• Yeah I corrected it. It would be great if you could answer it too. – stochastic_zeitgeist Dec 5 '14 at 10:45
• Sorry, what is the question exactly ? – TZDZ Dec 5 '14 at 10:52
• well, in your reasoning, every vector is tangent to any circle... – TZDZ Dec 7 '14 at 10:48
• I'm voting to close this question as off-topic because it's more about the definition of a tangent than about physics. – Michael Seifert May 10 at 12:42