Tag: electromagnetic induction

Quizzes (6) Questions (197)

Questions Related to electromagnetic induction

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

The coefficient of self induction of two inductor coils are $20mH$ and $40mH$ respectively. If the coils are connected in series so as to support each other and the resultant inductance is $80mH$ then the value of mutual inductance between the coils will be

  1. $5mH$
  2. $10mH$
  3. $20mH$
  4. $40mH$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$L _{total} = L _1 + L _2 + 2M$


$80 mH = 20 mH + 40 mH + 2M$

$\therefore M = 10 mH$

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

A rectangular loop of sides 'a' and 'b' is placed in the XY plane. A very long wire is also placed in xy plane such that side of length 'a' of the loop is parallel to the wire. The distance between the wire and the nearest edge of the loop is 'd'. The mutual inductance of this system is proportional to?

  1. a

  2. b
  3. $1/d$

  4. Current in wire
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The mutual inductance M between a long wire and a rectangular loop is calculated by integrating the magnetic flux through the loop. The flux is proportional to the dimensions of the loop, specifically the side length 'a' parallel to the wire, because the magnetic field B varies with distance from the wire. Thus, M is proportional to 'a'.

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

A circular loop of radius $r$ is placed at the centre of current carrying conducting square loop of side $a$. If both loops are coplanar and $a >> r$, then the mutual inductance between the loops will be:

  1. $\dfrac{\mu _0r^2}{2\sqrt{2}(a)}$
  2. $\dfrac{\mu _0r^2}{4a}$
  3. $\dfrac{2\sqrt{2}\mu _0r^2}{\pi a}$
  4. $\dfrac{\mu _0r^2}{4\sqrt{2}a}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Both loops are coplanar. 

Magnetic field at the center of outer square current carrying loop is
${ B } _{ 1 }=\dfrac { 2\sqrt { 2 } { \mu  } _{ 0 }I }{ \pi a } $
where $a$= length of side of square loop and
$r$= radius of the circular loop.
Given $a>>r$,
The magnetic field through entire inner coil is ${ B } _{ 1 }$
Magnetic flux through inner coil, ${ \phi  } _{ 21 }={ B } _{ 1 }{ A } _{ 2 }$
        =$\dfrac { 2\sqrt { 2 } { \mu  } _{ 0 }I }{ \pi  } \dfrac { { r }^{ 2 } }{ a } $------ (1)
    Mutual induction, M= $\dfrac { \phi  }{ { I } _{ 1 } } $

From (1), M= $\dfrac { 2\sqrt { 2 } { \mu  } _{ 0 } }{ \pi  } \dfrac { { r }^{ 2 } }{ a } $

Hence, $M\alpha \dfrac { { r }^{ 2 } }{ a } $

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

A $50\ Hz$ $AC$ current of crest value $1\ A$ flows, through the primary of transformer. If the mutual inductance between the primary and secondary be $0.5\ H$, the crest voltage induced  in the secondary is

  1. 75 V

  2. 150 V

  3. 100 V

  4. 300V
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The induced crest voltage in the secondary coil is given by E_s = M * (di/dt)_max. The rate of change of current is di/dt = omega * I_0 = (2 * pi * f) * I_0. Substituting M = 0.5 H, f = 50 Hz, and I_0 = 1 A gives E_s = 0.5 * (2 * pi * 50 * 1) = 50 * pi approx 150.7 V, which rounds to 150 V.

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

Which of the following statement is correct?

  1. when the magnetic flux linked with conducting loop is zero then emf induced is always zero

  2. when the emf induced in conducting loop is zero, then the magnetic flux linked with the loop must be zero

  3. transformer works on mutual induction

  4. all of these
Reveal answer Fill a bubble to check yourself
A,C Correct answer
Explanation

 Statement is.

A) When the magnetic flux linked with conducting loop is zero then emf induced is always zero.
     $emf=\dfrac{d\phi}{dt}$
  If $\phi=0$, $emf=\dfrac{d0}{dt}=0$
B) when the emf induced in conducting loop is zero, then the magnetic flux linked with the loop must be zero.
    $emf=\dfrac{d\phi}{dt}=0$
    $d\phi=0$
   $\phi=constant$ magnetic flux is constant.
This is the wrong statement
C) The transformer works on mutual induction.
The correct statement is (A) and (C).


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

An electron originates at a point $A$ lying on the axis of a straight solenoid and moves with velocity $v$ at an angle $\alpha$ to the axis. The magnetic induction of the field is equal to $BA$ screen is oriented at right angles to the axis and is located at a distance $1$ from the point $a$. Find the distance from the axis to the point on the screen into which the electron strikes.

  1. $d = 5r\sin \left (\dfrac {\theta}{2}\right )$, Here $r = 2\dfrac {mv\sin \alpha}{eB}$ and $\theta = \dfrac {eBl}{mv\cos \alpha}$.
  2. $d = 2r\sin \left (\dfrac {\theta}{2}\right )$, Here $r = \dfrac {mv\sin \alpha}{eB}$ and $\theta = \dfrac {eBl}{mv\cos \alpha}$.
  3. $d = 3r\sin \left (\dfrac {\theta}{2}\right )$, Here $r = 3\dfrac {mv\sin \alpha}{eB}$ and $\theta = \dfrac {eBl}{mv\cos \alpha}$.
  4. $d = 4r\sin \left (\dfrac {\theta}{2}\right )$, Here $r = \dfrac {mv\sin \alpha}{eB}$ and $\theta = \dfrac {eBl}{mv\cos \alpha}$.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The electron moves in a helical path in a uniform magnetic field. The radius of the helix is r = (mv*sin(alpha))/(eB) and the pitch angle/period determines the displacement. The distance from the axis is calculated using the geometry of the circular projection of the helical motion.

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

Two conducting circular loops of radii $R _{1}$ and $R _{2}$ are placed in the same plane with their centres coinciding. If $R _{1} \gg R _{2}$, the mutual inductance $M$ between them will be directly proportional to

  1. $R _{1}/R _{2}$
  2. $R _{2}/R _{1}$
  3. $R _{1}^{2}/R _{2}$
  4. $R _{2}^{2}/R _{1}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For two concentric loops where R1 >> R2, the magnetic field produced by the larger loop (R1) at its center is B = (mu0 * I) / (2 * R1). The flux through the smaller loop is Phi = B * Area2 = (mu0 * I * pi * R2^2) / (2 * R1). Since M = Phi / I, M = (mu0 * pi * R2^2) / (2 * R1), which is proportional to R2^2 / R1.

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

The mutual inductance $M _{12}$ of coil 1 with respect to coil 2

  1. increases when they are bought nearer.

  2. depends on the current passing through the coils.

  3. increases when one of them is rotated about an axis.
  4. is not same as $M _{21}$ of coil 2 with respect to coil 1.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Mutual inductance depends on the geometry, orientation, and separation of the coils. Bringing them closer increases the magnetic flux linkage between them, thereby increasing the mutual inductance.