A circular wire loop of radius $R$ is placed in the $x$-y plane centered at the origin $O. A$ square loop os side $a ( a << R$ ) having two turns is placed with its center at $a=\sqrt{3} \ R$ along the axis of the circular wire loop, as shown in figure. The plane of the square loop makes an angle of $45^{\circ}$ with respect to the $z$-axis. If the mutual inductance between the loops is given by
$\frac{\mu_0 a^2}{2^{p / 2} R}$, then the value of $p$ is
A circular wire loop of radius $R$ is placed in the $x$-y plane centered at the origin $O. A$ square loop os side $a ( a << R$ ) having two turns is placed with its center at $a=\sqrt{3} \ R$ along the axis of the circular wire loop, as shown in figure. The plane of the square loop makes an angle of $45^{\circ}$ with respect to the $z$-axis. If the mutual inductance between the loops is given by
$\frac{\mu_0 a^2}{2^{p / 2} R}$, then the value of $p$ is
- [IIT 2012]
- A
$6$
- B
$7$
- C
$8$
- D
$9$
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- [KVPY 2019]
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- [JEE MAIN 2024]
$(a)$ Obtain an expression for the mutual inductance between a long straight wire and a square loop of side $a$ as shown in Figure.
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$(a)$ Obtain an expression for the mutual inductance between a long straight wire and a square loop of side $a$ as shown in Figure.
$(b)$ Now assume that the straight wire carries a current of $50\; A$ and the loop is moved to the right with a constant velocity, $v=10 \;m / s$ Calculate the induced $emf$ in the loop at the instant when $x=0.2\; m$ Take $a=0.1\; m$ and assume that the loop has a large resistance.