Tag: motional emf

Questions Related to motional emf

 A coil of circular cross-section having $100$ turns and $4 \mathrm { cm } ^ { 2 }$ face area is placed with its axis parallel to a magnetic field which decreases by $10 ^ { - 2 } \mathrm { Wb } \mathrm { m } ^ { - 2 }$ in $0.01 \mathrm { s }$. The e.m.f induced in the coil is: 

motional emf physics

  1. $200 \mathrm { mV }$

  2. $0.4 \mathrm { mV }$

  3. $400 \mathrm { mV }$

  4. $4 \mathrm { mV }$

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Correct Option: A

Radius of current carrying coil is 'R'. The ratio of magnetic field at a axial point which is R distance away from the centre of the coil to the magnetic field at the centre of the coil :-

motional emf physics

  1. $\lgroup \frac{1}{2} \rgroup^{1/2}$

  2. $\frac{1}{2}$

  3. $\lgroup \frac{1}{2} \rgroup^{3/2}$

  4. $\frac{1}{4}$

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Correct Option: C
Explanation:

$\begin{array}{l} \vec { B } \, at\, R\, dis\tan  ce=\frac { { { \mu _{ o } }I{ R^{ 2 } } } }{ { 2{ { \left( { { x^{ 2 } }+{ R^{ 2 } } } \right)  }^{ 3/2 } } } }  \ =\frac { { { \mu _{ o } }I{ R^{ 2 } } } }{ { 2{ { \left( { 2{ R^{ 2 } } } \right)  }^{ 3/2 } } } }  \ =\frac { { { \mu _{ o } }I{ R^{ 2 } } } }{ { 2.{ { \left( 8 \right)  }^{ 1/2 } }.{ R^{ 3 } } } }  \ =\frac { { { \mu _{ o } }i } }{ { 4\sqrt { 2 } R } }  \ \vec { B } \, \, at\, \, centre=\frac { { { \mu _{ o } }i } }{ { 2R } }  \ Ratio=\frac { { { \mu _{ o } }i.2R } }{ { 4\sqrt { 2 } R.{ \mu _{ o } }i } } =\frac { 1 }{ { 2\sqrt { 2 }  } } ={ \left( { \frac { 1 }{ 2 }  } \right) ^{ 3/2 } } \ Hence, \ option\, \, C\, \, is\, \, correct\, \, answer. \end{array}$

The magnetic induction due to a magnet on the equatorial line at a distance 0.2 m is $54 \times 10^{-6}$T. The magnetic induction at 0.3m is

motional emf physics

  1. $1.6 \times 10^{-6} \quad T$

  2. $1.6 \times 10^{-5} \quad T$

  3. $3.2 \times 10^{-6} \quad T$

  4. $3.2 \times 10^{-5} \quad T$

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Correct Option: B

A uniform metal rod is moving with a uniform velocity $v$ parallel to a long straight wire carrying a current $I$. The rod is perpendicular to the wire with its ends at distances $r _{1}$ and $r _{2}$ with $(r _{2} > r _{1})$ from it. The emf induced in the rod is

motional emf physics

  1. Zero

  2. $\dfrac {\mu _{0}Iv}{2\pi}\log _{e}\left (\dfrac {r _{2}}{r _{1}}\right )$

  3. $\dfrac {\mu _{0}Iv}{2\pi}\log _{e}\left (\dfrac {r _{1}}{r _{2}}\right )$

  4. $\dfrac {\mu _{0}Iv}{4\pi}\left (1 - \dfrac {r _{1}}{r _{2}}\right )$

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Correct Option: B

If the permeability of iron piece is $3 \times 10 ^ { - 3 }$ and intensity of magnetising field of iron piece is 120 A/m, then what is the magnetic induction of iron piece 

motional emf physics

  1. $0.36 \mathrm { Wb } / \mathrm { m } ^ { 2 }$

  2. $5 \times 10 ^ { - 3 } \mathrm { Wb } / \mathrm { m } ^ { 2 }$

  3. $40 \mathrm { Wb } / \mathrm { m } ^ { 2 }$

  4. $2.5 \times 10 ^ { - 4 } \mathrm { Wb } / \mathrm { m } ^ { 2 }$

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Correct Option: A

A conducting ring of radius r is placed perpendicularly inside a time verying magnetic field given by $B={ B } _{ 0 }+\alpha t.{ B } _{ 0 }$ and $\alpha $ are positive constants. E. m. f induced in the ring is 

motional emf physics

  1. $-\pi \alpha r$

  2. $-\pi \alpha { r }^{ 2 }$

  3. $-\pi { \alpha }^{ 2 }{ r }^{ 2 }$

  4. $-\pi { \alpha }^{ 2 }{ r }$

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Correct Option: B

In the figure magnetic points into the plane of paper and the rod of length $l$ is moving in the field such that the bottom most point has a velocity $v _1$ and the topmost point has the velocity $V _2(V _2>V _1)$ The emf induced is given by 

motional emf physics

  1. $Bv _1l$

  2. $Bv _2l$

  3. $\cfrac 1 2 B(v _2+v _1)l$

  4. $\cfrac 1 2 B(v _2-v _1)l$

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Correct Option: C
Explanation:
Velocity of a point at a distance $x$ from the bottom is given by,

$v=v _1+(\dfrac{v _1-v _2}{l})x$

Potential difference on a small length at this distance is $e=Bx(dx)$

Therefore,

Total potential difference, $e=\int^l _0 Bvdx$

$e=\int^l _0 B(v _1+\dfrac{(v _2-v _1)x}{l})dx$

$=\dfrac{B(v _1+v _2)l}{2}$

A uniform magnetic field exists in region given by $\vec B = 3\hat i + 4\hat j + 5\hat k$. A rod of length $5m$ is placed along $y$ moved along $x-axis$ with constant speed $1m/sec$. Then induced e.m.f. in the rod will be:

motional emf physics

  1. $zero$

  2. $25V$

  3. $20V$

  4. $15V$

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Correct Option: B

A square coil of side 0.5$\mathrm { m }$ has movable side It is placed such that its plane is perpendicularuniform magnetic field of induction 0.2$\mathrm { T }$ . If all sides are allowed to move with a speed of 0.1for 4 sec outwards, average indaced emf is

motional emf physics

  1. Zero

  2. 0.01$\mathrm { V }$

  3. 0.028$\mathrm { V }$

  4. 0.072$\mathrm { V }$

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Correct Option: D

The amplitude of a magnetic field, which is part of a harmonic electromagnetic wave in vacuum, is  $\mathrm { B } _ { 0 } =510\mathrm { nT } .$  What is the amplitude of the electric field of the wave? 

motional emf physics

  1. $140 \mathrm { NC } ^ { - 1 }$

  2. $153 \mathrm { NC } ^ { - 1 }$

  3. $163 \mathrm { NC } ^ { - 1 }$

  4. None of these

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Correct Option: B