Electromagnetic induction - Live Session - 05 Sept 2020Contact Number: 9667591930 / 8527521718

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A coil has, 1,000 turns and 500 $c{m}^{2}$ as its area. The plane of the coil is placed at right angles to a magnetic field of $2\times {10}^{-5}Wb/{m}^{2}$. The coil is rotated through 180$\xb0$ in 0.2. The average e.m.f. induced in the coil, in milli-volts, is

1. 5

2. 10

3. 15

4. 20

In a circuit with a coil of resistance 2 *ohms*, the magnetic flux changes from 2.0 *Wb* to 10.0 *Wb* in 0.2 second. The charge that flows in the coil during this time is

(1) 5.0 *coulomb*

(2) 4.0 *coulomb*

(3) 1.0 *coulomb*

(4) 0.8 *coulomb*

An aluminum ring *B* faces an electromagnet *A*. The current *I* through *A* can be altered. Then :

(1) Whether *I* increases or decreases, *B* will not experience any force

(2) If *I* decrease, *A* will repel *B*

(3) If *I* increases, *A* will attract *B*

(4) If *I* increases, *A* will repel *B*

An electric potential difference will be induced between the ends of the conductor shown in the diagram when the conductor moves in the direction

(1) *P *

(2) *Q*

(3) *L *

(4) *M*

A conducting square loop of side *L* and resistance *R* moves in its plane with a uniform velocity *v* perpendicular to one of its sides. A magnetic induction *B* constant in time and space, pointing perpendicular and into the plane of the loop exists everywhere. The current induced in the loop is:** **

1. $\frac{Blv}{R}$ clockwise

2. $\frac{Blv}{R}$ anticlockwise

3. $\frac{2Blv}{R}$ anticlockwise

4. Zero

A thin semicircular conducting ring of radius *R* is falling with its plane vertical in a horizontal magnetic induction *B*. At the position *MNQ*, the speed of the ring is *v* and the potential difference developed across the ring is:** **

1. Zero

2. $Bv\pi {R}^{2}/2$ and *M* is at the higher potential

3. 2*RBv* and M is at the higher potential

4. 2*RBv* and *Q* is at the higher potential

A uniform but time-varying magnetic field *B*(*t*) exists in a circular region of radius *a* and is directed into the plane of the paper, as shown. The magnitude of the induced electric field at point *P* at a distance *r* from the centre of the circular region

(1) Is zero

(2) Decreases as $\frac{1}{r}$

(3) Increases as *r*

(4) Decreases as $\frac{1}{{r}^{2}}$

A conducting rod of length 2*l* is rotating with constant angular speed *$\omega $* about its perpendicular bisector. A uniform magnetic field $\overrightarrow{B}$ exists parallel to the axis of rotation. The e.m.f. induced between two ends of the rod is

(1) *BΩl*^{2}

(2) $\frac{1}{2}B\omega {l}^{2}$

(3) $\frac{1}{8}B\omega {l}^{2}$

(4) Zero

A conducting wireframe is placed in a magnetic field that is directed into the paper. The magnetic field is increasing at a constant rate. The directions of induced current in wires *AB* and *CD* are:

1. B to *A* and *D* to *C*

2. *A* to *B* and *C* to *D*

3. *A* to *B* and *D* to *C*

4. *B* to *A* and *C* to *D*

Shown in the figure is a circular loop of radius *r* and resistance *R*. A variable magnetic field of induction *B* = *B*_{0}*e*^{–t} is established inside the coil. If the key (*K*) is closed, the electrical power developed right after closing the switch, at t=0, is equal to

(1) $\frac{{B}_{0}^{2}\pi {r}^{2}}{R}$

(2) $\frac{{B}_{0}10{r}^{3}}{R}$

(3) $\frac{{B}_{0}^{2}{\pi}^{2}{r}^{4}R}{5}$

(4) $\frac{{B}_{0}^{2}{\pi}^{2}{r}^{4}}{R}$

A rectangular loop with a sliding connector of length *l* = 1.0 *m* is situated in a uniform magnetic field *B* = 2 *T* perpendicular to the plane of the loop. Resistance of connector is *r* = 2 Ω. Two resistance of 6 Ω and 3 Ω are connected as shown in the figure. The external force required to keep the connector moving with a constant velocity *v* = 2 *m/s* is:

1. 6 *N*

2. 4 *N*

3. 2 *N*

4. 1 *N *

A conducting rod *AC* of length 4*l* is rotated about a point *O* in a uniform magnetic field $\overrightarrow{B}$ directed into the paper. *AO* = *l* and *OC* = 3*l*. Then

(1) ${V}_{A}-{V}_{O}=\frac{B\omega {l}^{2}}{2}$

(2) ${V}_{O}-{V}_{C}=\frac{7}{2}B\omega {l}^{2}$

(3) ${V}_{A}-{V}_{C}=4B\omega {l}^{2}$

(4) ${V}_{C}-{V}_{O}=\frac{9}{2}B\omega {l}^{2}$

A simple pendulum with bob of mass *m* and conducting wire of length *L* swings under gravity through an angle 2*θ*. The earth’s magnetic field component in the direction perpendicular to swing is *B*. Maximum potential difference induced across the pendulum is

(1) $2BL\mathrm{sin}\left(\frac{{\displaystyle \theta}}{{\displaystyle 2}}\right){\left(gL\right)}^{1/2}$

(2) $BL\mathrm{sin}\left(\frac{{\displaystyle \theta}}{{\displaystyle 2}}\right){\left(gL\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$

(3) $BL\mathrm{sin}\left(\frac{{\displaystyle \theta}}{{\displaystyle 2}}\right){\left(gL\right)}^{3/2}$

(4) $BL\mathrm{sin}\left(\frac{{\displaystyle \theta}}{{\displaystyle 2}}\right){\left(gL\right)}^{2}$

Some magnetic flux is changed from a coil of resistance 10 *ohm*. As a result an induced current is developed in it, which varies with time as shown in figure. The magnitude of change in flux through the coil in *webers* is

(1) 2

(2) 4

(3) 6

(4) None of these

Figure (i) shows a conducting loop being pulled out of a magnetic field with a speed *v*. Which of the four plots shown in figure (ii) may represent the power delivered by the pulling agent as a function of the speed *v*

(1) *a*

(2) *b *

(3) *c*

(4) *d *

An electron moves on a straight-line path XY as shown. The abcd is a coil adjacent to the path of the electron. What will be the direction of the current, if any induced in the coil?

1. | abcd |

2. | adcb |

3. | The current will reverse its direction as the electron goes past the coil. |

4. | No current is induced. |

A coil having number of turns N and cross-sectional area A is rotated in a uniform magnetic field B with an angular velocity $\mathrm{\omega}$. The maximum value of the emf induced in it is –

1. $\frac{\mathrm{NBA}}{\mathrm{\omega}}$

2. $\mathrm{NBA\omega}$

3. $\frac{\mathrm{NBA}}{{\mathrm{\omega}}^{2}}$

4. ${\mathrm{NBA\omega}}^{2}$

The back emf induced in a coil, when current changes from 1 ampere to zero in one milli-second, is 4 volts. The self-inductance of the coil is:

1. $1H$

2. $4H$

3. ${10}^{\u20133}H$

4. $4\times {10}^{\u20133}H$

A wooden stick of length $3\mathcal{l}$ is rotated about an end with constant angular velocity $\mathrm{\omega}$ in a uniform magnetic field B perpendicular to the plane of motion. If the upper one third of its length is coated with copper, the potential difference across the whole length of the stick is –

1. $\frac{9\mathrm{B\omega}{\mathcal{l}}^{2}}{2}$

2. $\frac{4\mathrm{B\omega}{\mathcal{l}}^{2}}{2}$

3. $\frac{5\mathrm{B\omega}{\mathcal{l}}^{2}}{2}$

4. $\frac{\mathrm{B\omega}{\mathcal{l}}^{2}}{2}$

PQ is an infinite current carrying conductor. AB and CD are smooth conducting rods on which a conductor EF moves with constant velocity v as shown. The force needed to maintain constant speed of EF is –

1. $\frac{1}{\mathrm{VR}}{\left[\frac{{\mathrm{\mu}}_{0}Iv}{2\mathrm{\pi}}\mathrm{ln}\left(\frac{\mathrm{b}}{\mathrm{a}}\right)\right]}^{2}$

2. $\frac{1}{\mathrm{VR}}{\left[\frac{{\mathrm{\mu}}_{0}Iv}{2}\mathrm{ln}\left(\frac{\mathrm{b}}{\mathrm{a}}\right)\right]}^{2}$

3. $\frac{\mathrm{V}}{\mathrm{R}}{\left[\frac{{\mathrm{\mu}}_{0}\mathrm{IV}}{2}\mathrm{ln}\left(\frac{\mathrm{b}}{\mathrm{a}}\right)\right]}^{2}$

4. $\frac{\mathrm{V}}{\mathrm{R}}{\left[\frac{{\mathrm{\mu}}_{0}\mathrm{IV}}{2\mathrm{\pi}}\mathrm{ln}\left(\frac{\mathrm{b}}{\mathrm{a}}\right)\right]}^{2}$

A circular ring of radius r is placed in a homogeneous magnetic field perpendicular to the plane of the ring. The field B changes with time according to the equation B = Kt, where K is a constant and t is the time. The electric field in the ring is

(1) $\frac{Kr}{4}$

(2) $\frac{Kr}{3}$

(3) $\frac{Kr}{2}$

(4) $\frac{K}{2r}$

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