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Since we all know that to increase the magnetic field we can do these of the following things:

(i) Increase the number of turns in a coil,

(ii) Increase the current following through conductor,

and there would be more but I know only these (upto my standard - Xth )

now if I use the first method to increase the magnetic field then the length of conductor will also increase because I am increasing the number of turns; say I am increasing the length of conductor by $x$ meters then as we all know that:

$R = \rho l/a$

you know resistance is equal to resistivity multiplied by length of conductor and then divided by the area of cross section.

According to this $R$ is directly propotional to length of conductor and by Ohm's law $R$ is inverously proportional to current

Therefore if I increase the length by $x$ m of conductor then the resistance will also increase at a rate of $x \Omega $ and current will decrease at $x$ Ampere, then how will the magnetic field increase if the current is being reduced?

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Increasing the number of turns increases the magnetic field if the current remains constant. In your situation, you are postulating (implicitly) that the applied voltage is constant, and that the current is reduced. The product $N\cdot I$ is therefore unchanged, and the magnetic field does not increase when you increase the number of turns of a resistive wire.

Note - for some of the largest magnets used in medical imaging, they use superconducting wire...

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resistance will be R=rho(l+x)/a. it wont increase with a factor of x as in you are not multiplying the additional turns. though the resistance increase but the magnetic field strength increases more.

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    $\begingroup$ I think a more extensive explanation would be better. $\endgroup$ – Danu Nov 15 '15 at 18:57
  • $\begingroup$ Welcome to Physics! Note that this site has MathJax enabled, which means you can use Latex-like syntax to add in equations for readability. $\endgroup$ – Kyle Kanos Nov 15 '15 at 21:06
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What's important to remember is that in most electrical circuits, the total resistance is not just the coil. In fact, just a coil, in a direct current circuit, would be a short circuit and draw enormous current and blow a fuse or destroy something in the circuit. In such a circuit, increasing the number of turns in the coil would increase resistance by the same factor and the magnetic field would stay the same. But most circuits are not just a coil. They have some other resistive elements that are not part of the coil. Then the equation looks like Rt=R1 + R2, where R2=rho(L)/A. In most cases R2 is a small fraction of Rt, so doubling the number of turns (and subsquently R2) will not half the current, and so magnetism increases.

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Because of magnetic field attraction towards the coil.

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  • $\begingroup$ This doesn't really answer the question. $\endgroup$ – Jon Custer Oct 3 '15 at 17:44

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