(A) The magnetic field at the center of a circular coil of $n$ turns is given by $B = \frac{\mu_0 n I}{2R}$.For a wire of length $L$,the radius $R$ of

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(A) The magnetic field at the center of a circular coil of $n$ turns is given by $B = \frac{\mu_0 n I}{2R}$.For a wire of length $L$,the radius $R$ of a single-turn loop is $R = \frac{L}{2\pi}$. Thus,$B = \frac{\mu_0 I}{2(L/2\pi)} = \frac{\mu_0 \pi I}{L}$.When the same wire is formed into a loop of $n$ turns,the new radius $R'$ is $R' = \frac{L}{2\pi n} = \frac{R}{n}$.The new magnetic field $B'$ is $B' = \frac{\mu_0 n I}{2R'} = \frac{\mu_0 n I}{2(R/n)} = n^2 \left( \frac{\mu_0 I}{2R} \right) = n^2 B$.Given $n = 3$,the new magnetic field is $B' = 3^2 B = 9B$.

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

Medium

$A$ linear wire carries a current $I$. $A$ single-turn loop is formed from it,and the magnetic field at the center is $B$. If a three-turn loop is formed from the same wire,what will be the magnetic field at the center?

A
$9B$
B
$\frac{1}{9}B$
C
$3B$
D
$\frac{1}{3}B$

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Moving Charges and Magnetism

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Biot-Savart's Law and its application

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DifficultTS EAMCET 2009

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$A$ linear wire carries a current $I$. $A$ single-turn loop is formed from it,and the magnetic field at the center is $B$. If a three-turn loop is formed from the same wire,what will be the magnetic field at the center?

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