Tag: mutual inductance

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Multiple choice mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

A conducting ring of radius r and resistance R rolls on a horizontal surface with constant velocity v. 

  1. The induced emf.between O and Q is 2 Bvr.
  2. An induced current $ I= \dfrac { 2Bvr }{ R } $ flows in the clockwise direction.
  3. An induced current $ I= \dfrac { 2Bvr }{ R } $ flows in the anticlockwise direction.

  4. No current flows
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

When a conducting ring rolls on a surface, the motional emf induced in the top half cancels the emf induced in the bottom half relative to the center, or the symmetry of the rolling motion results in zero net current in the ring.

Multiple choice mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

Mutual inductance of a system of two thin coaxial conducting loops of radius each, their centers separated by distance $d (d >>r)$ is 

  1. $\mu _0\pi r^4d^3$
  2. $\dfrac{\mu _0\pi r^4}{2d^3}$
  3. $\dfrac{\mu _0\pi r^4}{d^3}$
  4. $\dfrac{\mu _0\pi r^4 d^3}{4}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The mutual inductance between two small coaxial loops separated by distance d is M = (mu_0 * pi * r1^2 * r2^2) / (2 * d^3). Given r1 = r2 = r, M = (mu_0 * pi * r^4) / (2 * d^3).

Multiple choice mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

The coefficient of mutual inductance, when magnetic flux changes by $\displaystyle 2\times { 10 }^{ -2 }Wb$ and current changes by 0.01 A is :

  1. 8 henry

  2. 4 henry

  3. 3 henry

  4. 2 henry
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

We know that

$\displaystyle \phi =Mi$
$\displaystyle d\phi =Mdi$

$\displaystyle M=\frac { d\phi  }{ di } =\frac { 2\times { 10 }^{ -2 } }{ 1\times { 10 }^{ -2 } } =2$ henry