(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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The magnetic field due to a current-carrying circular loop of radius $6 \ cm$ at a point on the axis at a distance of $8 \ cm$ from the centre is $216 \ \mu T$. Then the magnetic field at the centre of the ring is $\dots \ \mu T$.

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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

Two circular coils are made from the same wire,but the radius of the $1^{\text{st}}$ coil is twice that of the $2^{\text{nd}}$ coil. If the magnetic field at their centers is the same,then the ratio of the potential difference applied across them is ($1^{\text{st}}$ to $2^{\text{nd}}$ coil).

There are two infinitely long straight current-carrying conductors held at right angles to each other such that their common ends meet at the origin, as shown in the figure. The ratio of current in both conductors is $1:1$. The magnetic field at point $P(x, y)$ is:

Two concentric coils of $10$ turns each are placed in the same plane. Their radii are $20 \ cm$ and $40 \ cm$ and carry $0.2 \ A$ and $0.3 \ A$ current respectively in opposite directions. The magnetic induction (in $T$) at the centre is

The magnetic field due to a current-carrying circular loop of radius $6 \ cm$ at a point on the axis at a distance of $8 \ cm$ from the centre is $216 \ \mu T$. Then the magnetic field at the centre of the ring is $\dots \ \mu T$.

Magnetic field intensity at the centre of a coil of $50$ turns,radius $0.5\, m$ and carrying a current of $2\, A$ is:

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