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# In an experiment using tangent galvanometer, the magnetic induction is measured at various points on the axis of a current carrying circular coil on both sides of the center O of the coil. The variation of magnetic field along the axis is best represented in the curve:A. B. C. D.

Last updated date: 11th Jun 2024
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Hint: In a current carrying coil the electric current creates a magnetic field which is more concentrated in the center of the coil than outside the loop. According to Biot-Savart’s law, the magnetic field at a point due to an element of a conductor carrying current is,
-Directly proportional to the strength of the current.
-Directly proportional to the length of the element.
-Directly proportional to the Sine of the angle between the element and the line joining the element to the point.
-Inversely proportional to the square of the distance between the element and the point.

Let us assume that the radius of the coil be R.
Then the magnetic field at distance r on the axis of coil is given by,
$B = \dfrac{{{\mu _o}I{R^2}}}{{2{{({r^2} + {R^2})}^{\dfrac{3}{2}}}}}$
Now when $r > > R$
$B = \dfrac{{{\mu _o}I{R^2}}}{{2{r^3}}}$
Since radius of the coil and current are constant we can say that,
$B \propto \dfrac{1}{{{r^3}}}......(1)$
Now at the center of the coil we have,
$r = R$
Hence, the expression for magnetic field becomes
$B = \dfrac{{{\mu _o}I{r^2}}}{{{r^3}}} \\ \Rightarrow B = \dfrac{{{\mu _o}I}}{r} \\$
Since, current is constant Therefore, we have
$B \propto \dfrac{1}{r}......(2)$
From (1) and (2) we can observe that the plot for magnetic field due to current carrying coil is
$\begin{array}{*{20}{c}} B& \propto &{\left\{ {\begin{array}{*{20}{c}} {\dfrac{1}{{{r^3}}}}&{r > > R} \\ {\dfrac{1}{r}}&{r = R} \end{array}} \right\}} \end{array}$
It is clear from the above equations that option B is the correct representation.

Note:When a current flows in a wire, it creates a circular magnetic field around the wire. This magnetic field can deflect the needle of a magnetic compass. The strength of a magnetic field is directly proportional to the current flowing. Therefore, if an alternating current is flowing, a magnetic field around the conductor will be produced, that is in phase with the alternating current.