(C) Let the length of the wire be $L$. For a single turn,the radius $R$ is given by $L = 2 \pi R$,so $R = L / (2 \pi)$. The magnetic field at the cent

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(C) Let the length of the wire be $L$. For a single turn,the radius $R$ is given by $L = 2 \pi R$,so $R = L / (2 \pi)$. The magnetic field at the center is $B = \frac{\mu_0 I}{2R} = \frac{\mu_0 I}{2(L / 2 \pi)} = \frac{\mu_0 I \pi}{L}$.When the same wire is bent into $n$ turns,the new radius $r_1$ is given by $L = n(2 \pi r_1)$,so $r_1 = L / (2 \pi n) = R / n$.The magnetic field at the center for $n$ turns is $B' = n \frac{\mu_0 I}{2 r_1}$.Substituting $r_1 = R / n$,we get $B' = n \frac{\mu_0 I}{2 (R / n)} = n^2 \frac{\mu_0 I}{2 R} = n^2 B$.

Class 12 Physics Moving Charges and Magnetism Biot-Savart's Law and its application

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$A$ long wire carrying a steady current is bent into a circle of single turn. The magnetic field at the centre of the coil is $B$. If it is bent into a circular loop of radius $r_1$ having $n$ turns,the magnetic field at the centre of the coil for the same current is:

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A
$B/n^2$
B
$B/n$
C
$n^2 B$
D
$n B$

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Moving Charges and Magnetism

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Biot-Savart's Law and its application

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$A$ long wire carrying a steady current is bent into a circle of single turn. The magnetic field at the centre of the coil is $B$. If it is bent into a circular loop of radius $r_1$ having $n$ turns,the magnetic field at the centre of the coil for the same current is:

Similar Questions

The direction of magnetic lines of force produced by passing a direct current in a conductor is given by

$A$ steady current $I$ flows through a wire loop $PQR$ having the shape of a right-angled triangle with $PQ = 3x$, $PR = 4x$, and $QR = 5x$. If the magnitude of the magnetic field at $P$ due to this loop is $k \left( \frac{\mu_0 I}{48 \pi x} \right)$, find the value of $k$.

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$A$ circular arc of radius $r$ carrying current $I$ subtends an angle $\frac{\pi}{16}$ at its centre. The radius of the metal wire is uniform. The magnetic induction at the centre of the circular arc is [where $\mu_0$ is the permeability of free space].

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