$AB$ is an infinitely long wire placed in the plane of rectangular coil of dimensions as shown in the figure. Calculate the mutual inductance of wire $AB$ and coil $PQRS$
$AB$ is an infinitely long wire placed in the plane of rectangular coil of dimensions as shown in the figure. Calculate the mutual inductance of wire $AB$ and coil $PQRS$
- A
$\frac{{{\mu _0}b}}{{2\pi }}\ln \frac{a}{b}$
- B
$\frac{{{\mu _0}c}}{{2\pi }}\ln \frac{b}{a}$
- C
$\frac{{{\mu _0}abc}}{{2\pi {{\left( {b - a} \right)}^2}}}$
- D
None of these
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The mutual inductance between two coils is $1.25$ $henry$. If the current in the primary changes at the rate of $80$ $ampere/second,$ then the induced $e.m.f$ in the secondary is......$V$
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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
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- [IIT 2012]
$(a)$ 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.
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$(b)$ 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.
A small square loop of wire of side $l$ is placed inside a large square loop of wire $L(L \gg l)$. Both loops are coplanar and their centres coincide at point $O$ as shown in figure. The mutual inductance of the system is.
A small square loop of wire of side $l$ is placed inside a large square loop of wire $L(L \gg l)$. Both loops are coplanar and their centres coincide at point $O$ as shown in figure. The mutual inductance of the system is.
- [JEE MAIN 2022]
Two coils of self inductance ${L_1}$ and ${L_2}$ are placed closer to each other so that total flux in one coil is completely linked with other. If $M$ is mutual inductance between them, then $M$ is
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