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Physics-

General

Easy

Question

What is the mutual inductance of a two-loop system as shown with centre separation l

$\frac{μ_{0} π a^{4}}{8 l^{3}}$
$\frac{μ_{0} π a^{4}}{4 l^{3}}$
$\frac{μ_{0} π a^{4}}{6 l^{3}}$
$\frac{μ_{0} π a^{4}}{2 l^{3}}$

The correct answer is: $fraction numerator mu subscript 0 end subscript pi a to the power of 4 end exponent over denominator 2 l to the power of 3 end exponent end fraction$

Magnetic field at the location of coil (b) produced due to coil (a)

$B subscript 1 end subscript equals fraction numerator mu subscript o end subscript over denominator 4 pi end fraction. fraction numerator 2 M over denominator l to the power of 3 end exponent end fraction$
Flux linked with coil ((b)
$phi subscript 2 end subscript equals B subscript 1 end subscript A subscript 2 end subscript equals fraction numerator mu subscript o end subscript over denominator 4 pi end fraction fraction numerator 2 i left parenthesis pi a to the power of 2 end exponent right parenthesis over denominator l to the power of 3 end exponent end fraction cross times left parenthesis pi a to the power of 2 end exponent right parenthesis$
Also $phi subscript 2 end subscript equals M i$ $rightwards double arrow M equals fraction numerator mu subscript o end subscript pi a to the power of 4 end exponent over denominator 2 l to the power of 3 end exponent end fraction$

Related Questions to study

Assertion (A) : The length of latus rectum in fig is 24/5.

Reason (R) : If l₁ and l₂are length of segments of a focal chord of a parabola, then its latus rectum is $fraction numerator 4 l subscript 1 end subscript l subscript 2 end subscript over denominator l subscript 1 end subscript plus l subscript 2 end subscript end fraction$ .

Assertion (A) : The length of latus rectum in fig is 24/5.

Reason (R) : If l₁ and l₂are length of segments of a focal chord of a parabola, then its latus rectum is $fraction numerator 4 l subscript 1 end subscript l subscript 2 end subscript over denominator l subscript 1 end subscript plus l subscript 2 end subscript end fraction$ .

Assertion: Through ( $lambda comma lambda$ + 1) there can not the more than one normal to the parabola y² = 4x if + $lambda$ < 2.
Reason: The point ( $lambda comma lambda$ + 1) lie out side the parabola for all $lambda$ $not equal to$ 1.

Assertion: Through ( $lambda comma lambda$ + 1) there can not the more than one normal to the parabola y² = 4x if + $lambda$ < 2.
Reason: The point ( $lambda comma lambda$ + 1) lie out side the parabola for all $lambda$ $not equal to$ 1.

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