CBSE Questions for Class 12 Medical Physics Electromagnetic Induction Quiz 11 - MCQExams.com

For previous objective, which of the following graphs is correct
When a bar magnet is entered into a coil, thee induced emf in the coil does not depend upon:
  • Speed of magnet
  • number of turns in coil
  • Magnetic moment of magnet
  • Resistance of wire in coil
If a conducting rod moves with a constant velocity $$ v $$ in a magnetic field, emf is induced between both its ends if:
  • $$ v $$ and $$ B $$ are parallel
  • $$ v $$ is perpendicular to $$ \overrightarrow{B} $$
  • $$ v$$ and $$ B $$ are in opposite direction
  • All of the above
Induced $$ emf $$ of electromagnetic induction depends upon:
  • Resistance on conductor
  • The value of magnetic field
  • The direction of conductor $$ w.r.t. $$ the magnetic field
  • Rate of change of flux linked
What would be the coefficient of self-inductance of a coil $$ 100 turns, $$ if $$ 5 A $$ current flows through it? The magnetic flux is of $$ 5 \times 10^{3} $$ Maxwell.
  • $$ 0.5 \times 10^{-3} H $$
  • $$ 2 \times 10^{-3} H $$
  • $$ Zero $$
  • $$ 10^{-3}H $$
The phenomenon of electro-magnetic induction is
  • the process of charging a body.
  • the process of generating magnetic field due to a current passing through a coil.
  • producing induced current in a coil due to relative motion between a magnet and the coil.
  • the process of rotating a coil of an electric motor.
Electromagnetic induction is
  • Charging a substance.
  • Process of developing a magnetic field around a coil by passing electricity through a coil
  • Process of rotating the armature of a generator
  • Process of making electricity by the relative motion of a magnet or a coiled conductor.
Answer the question:
An e.m.f. is induced across a wire when it moves through the magnetic field between the poles of a magnet.
Which electrical device operates because of this effect ?
  • a battery
  • a cathode-ray tube
  • a generator
  • a motor
A conducting rod of length l moves with velocity v in x-direction axis parallel to a long wire carrying a steady current I. The axis of the rod is maintained perpendicular to the wire with near end a distance r away as shown in the fig. Find the emf induced in the rod. 
41901_4c34b54fcf0d4ac69ae4b6636cdc380e.png
  • $$\dfrac{\mu _{0}I\upsilon }{\pi }\, \, ln \left ( \frac{r+1}{r} \right )$$
  • $$\dfrac{2\mu _{0}I\upsilon }{\pi }\, \, ln \left ( \frac{r+1}{r} \right )$$
  • $$\dfrac{\mu _{0}I\upsilon }{\pi }\, \, ln \left ( \dfrac{l}{r+1} \right )$$
  • $$\dfrac{\mu _{0}I\upsilon }{ 2 \pi }\, \, ln \left ( \dfrac{r+1}{r} \right )$$
In a uniform magnetic field of induction $$B$$, a wire in the form of semicircle of radius $$r$$ rotates about the diameter of the circle with angular velocity $$\omega$$. If the total resistance of the circuit is $$R$$, the mean power generated per period of rotation is :
  • $$\dfrac{B\pi r^{2}\omega }{2R}$$
  • $$\dfrac{(B\pi r^{2}\omega)^{2} }{8R}$$
  • $$\dfrac{(B\pi r\omega)^{2} }{2R}$$
  • $$\dfrac{(B\pi r\omega^{2})^{2} }{8R}$$
A square metal wire loop of side 10 cm and of resistance 2 $$\Omega $$ moves with constant velocity in the presence of a uniform magnetic field of induction 4 T, perpendicular and into the plane of the loop. The loop is connected to a network of resistance as shown in the Figure. If the loop should have a steady current of 2 mA, the speed of the loop must be (in cm s$$^{-1}$$) :
44771_f85c525930be4d3c905839c74d81d775.png
  • $$4$$
  • $$2$$
  • $$3$$
  • $$6$$
A wire shaped as a semicircle of radius a is rotating about an axis PQ with a constant angular velocity $$\omega =\frac{1}{\sqrt{LC}}$$, with the help of an external agent. A uniform magnetic field B exists in space and is directed into the plane of the figure. (circuit part remains at rest (left part is at rest) ) . Then, 

73185.jpg
  • the rms value of current in the circuit is $$\dfrac{\pi Ba^{2}}{R\sqrt{2LC}}$$
  • the rms value of current in the circuit is $$\dfrac{\pi Ba^{2}}{2R\sqrt{LC}}$$
  • the maximum energy stored in the capacitor is $$\dfrac{\pi^{2} B^{2}a^{4}}{8R^{2}C}$$
  • the maximum power delivered by the external agent is $$\dfrac{\pi^{2} B^{2}a^{4}}{4LCR}$$
A semicircle conducting ring of radius R is placed in the xy plane, as shown in the figure. A uniform magnetic field is set up along the x-axis. No emf, will be induced in the ring if 
41960.jpg
  • it moves along the xaxis
  • it moves along the yaxis
  • it moves along the z-axis
  • All the above
Find the inductance of a unit length of two parallel wires, each of radius a, whose centers are at a distance d apart and carry equal currents in opposite directions. Neglect the flux within the wire:
  • $$\dfrac {\mu_0}{2\pi} ln \left (\dfrac {d-a}{a}\right )$$
  • $$\dfrac {\mu_0}{\pi} ln \left (\dfrac {d-a}{a}\right )$$
  • $$\dfrac {3\mu_0}{\pi} ln \left (\dfrac {d-a}{a}\right )$$
  • $$\dfrac {\mu_0}{3\pi} ln \left (\dfrac {d-a}{a}\right )$$
A rod AB moves with a uniform velocity $$v$$ in a uniform magnetic field as shown in figure.

76376_a03c60b87f784ec6a738b2e56b12ff91.png
  • The rod becomes electrically charged
  • The end A becomes positively charged
  • The end B become positively charged
  • The rod becomes hot because of Joule heating
The current i in a coil varies with time as shown in the figure. The variation of induced emf with time would be :
75600_e9eab6ae5ace45e792f9034abb0f06fa.png
A long solenoid having $$200$$ turns per cm carries a current of $$1.5 amp.$$ At the centre of it is placed a coil of $$100$$ turns of cross-sectional are $$3.14\times 10^{-4}m^2$$ having its axis parallel to the field produced by the solenoid. When the direction of current in the solenoid is reversed within $$0.05 sec,$$ the induced e.m.f. in the coil is
  • $$0.48 V$$
  • $$0.048 V$$
  • $$0.0048 V$$
  • $$48 V$$
A wire shaped as a circle of radius R rotates about the axis OO' with an angular velocity $$\omega$$ as shown in figure. Resistance of the circuit is $$R$$. Find the mean thermal power generated in the loop during a period of a rotation.
145816_091311d9a0864d8794fb85dfa1a3989b.JPG
  • $$\dfrac{(B \pi a^2 \omega)^2}{4R}$$
  • $$\dfrac{(B \pi a^2 \omega)^2}{2R}$$
  • $$\dfrac{(3B \pi a^2 \omega)^2}{2R}$$
  • None of these
A rectangular loop with a slide wire of length $$l$$ is kept in a uniform magnetic field as shown in figure (a). The resistance of slider is $$R$$. Neglecting self inductance of the loop find the current in the connector during its motion with a velocity $$v$$.
144698.png
  • $$\displaystyle \dfrac{Blv}{R_1 + R_2 + R}$$
  • $$\displaystyle \dfrac{Blv(R_1+ R_2)}{R(R_1 + R_2)}$$
  • $$\displaystyle \dfrac{Blv(R_1 + R_2)}{RR_1 + RR_2 + R_1R_2}$$
  • $$\displaystyle Blv \left ( \dfrac{1}{R_1} + \dfrac{1}{R_2} + \dfrac{1}{R_3}\right )$$
The potential difference across a $$150mH$$ inductor as a function of time is shown in figure. Assume that the initial value of the current in the inductor is zero. What is the current when $$t=4.0ms$$?
214051_84c1f037a8fb4989b089dbfd441471d8.png
  • $$2.67 \times 10^{-4}$$A
  • $$3.67 \times 10^{-2}$$A
  • $$6.67 \times 10^{-2}$$A
  • $$9.67 \times 10^{-4}$$A
A solenoid has $$2000$$ turns wound over a length of $$0.3 m$$. Its cross-sectional area is equal to $$1.2\times 10^{-3} m^2$$. Around its central cross-section, a coil of 300 turns is wound. If an initial current of $$2 A$$ flowing in the solenoid is reversed in $$ 0.25 s$$, the emf induced in the coil is
  • $$0.6 mV$$
  • $$60 mV$$
  • $$40.2 mV$$
  • $$0.48 mV$$
Find the inductance of a solenoid of length $$l_0$$, made of Cu windings of mass $$m$$. The winding resistance is equal to $$R$$. The diameter of solenoid << $$l$$. $$\rho_0$$ is resistivity of Cu and $$\rho$$ is density of the Cu.
  • $$\displaystyle \dfrac{\mu_0 Rm}{2 \pi l_0 \rho \rho_0}$$
  • $$\displaystyle \dfrac{\mu_0 Rm}{4 \pi l_0 \rho \rho_0}$$
  • $$\displaystyle \dfrac{\mu_0 Rm}{3 \pi l_0 \rho \rho_0}$$
  • $$\displaystyle \dfrac{2 \mu_0 Rm}{3 \pi l_0 \rho \rho_0}$$
A closed loop of cross-sectional area $$10^{-2}m^2$$ which has inductance $$L=10 mH$$ and negligible resistance is placed in a time-varying magnetic field. Figure shows the variation of B with time for the interval of 4 s. The field is perpendicular to the plane of the loop (given at $$t=0, B=0, I=0)$$. The value of the maximum current induced in the loop is :
120870_a3fbf048ba7542b4a6e79d20b5d6422e.png
  • 0.1 mA
  • 10 mA
  • 100 mA
  • Data insufficient
A metallic rod of length $$l$$ is hinged at the point $$M$$ and is rotating about an axis perpendicular to the plane of paper with a constant angular velocity $$\omega$$. A uniform magnetic field of intensity $$B$$ is acting in the region (as shown in the figure) parallel to the plane of paper. The potential difference between the points $$M$$ and $$N$$.
215082_3e082392f086432fb2e227cfe01098e0.png
  • is always zero
  • varies between $$\cfrac { 1 }{ 2 } B\omega { l }^{ 2 }$$ to $$0$$
  • is always $$\cfrac { 1 }{ 2 } B\omega { l }^{ 2 }$$
  • is always $$ B\omega { l }^{ 2 }$$
In the figure shown, a uniform magnetic field $$\left| \vec { B }  \right| =0.5T$$ is perpendicular to the plane of circuit. The sliding rod of length $$l=0.25m$$ moves uniformly with constant speed $$v=4 m{s}^{-1}$$. If the resistance of the slides is $$2\Omega$$, then the current flowing through the sliding rod is :

215240.PNG
  • $$0.1A$$
  • $$0.17A$$
  • $$0.08A$$
  • $$0.03A$$
An alternating current $$I$$ in an inductance coil varies with time $$t$$ according to the graph as shown:
Which one of the following graphs gives the variation of voltage with time?
215004_f79252cf8b8d4863853db54a1a6b4f5d.png
A conducting straight wire $$PQ$$ of length $$l$$ is fixed along a diameter of a non-conducting ring as shown in the figure. The ring is given a pure rolling motion on a horizontal surface such that its centre of mass has a veleocity $$v$$. There exists a uniform horizontal magnetic field $$B$$ in horizontal direction perpendicular to the plane of ring. The magnitude of induced emf in the wire $$PQ$$ at the position shown in the figure will be :

215145.PNG
  • $$Bvl$$
  • $$2Bvl$$
  • $$3Bvl/2$$
  • zero
Two metallic rings of radius $$R$$ are rolling on a metallic rod. A magnetic field of magnitude $$B$$ is applied in the region. The magnitude of potential difference between points $$A$$ and $$C$$ on the two rings (as shown), will be :

216019.PNG
  • $$0$$
  • $$4B\omega{R}^{2}$$
  • $$8B\omega{R}^{2}$$
  • $$2B\omega{R}^{2}$$
Choose the correct options
  • SI unit of magnetic flux is henry-ampere
  • SI unit of coefficient of self-inductance is $$J/A$$
  • SI unit of coefficient of self inductance is $$\cfrac{volt-second}{ampere}$$
  • SI unit of magnetic induction is weber
A straight conducting rod $$PQ$$ is executing SHM in $$xy$$ plane from $$x=-d$$ to $$x=+d$$. Its mean position is $$x=0$$ and its length is along y-axis. There exists a uniform magnetic field $$B$$ from $$x=-d$$ to $$x=0$$ pointing inward normal to the paper and from $$x=0$$ to $$=+d$$ there exists another uniform magnetic field of same magnitude $$B$$ but pointing outward normal to the plane of the paper. At the instant $$t=0$$, the rod is at $$x=0$$ and moving to the right. The induced emf $$(\varepsilon )$$ across the rod $$PQ$$ vs time $$(t)$$ graph will be
215119.PNG
A conducting ring of radius $$r$$ is rolling without slipping with a constant angular velocity $$\omega$$ (figure). If the magnetic field strength is $$B$$ and is directed into the page then the emf induced across $$PQ$$ is
222003_d51cbd3da8954cd49bf8a3c01d6bb466.png
  • $$B\omega {r}^{2}$$
  • $$\cfrac{B\omega{r}^{2}}{2}$$
  • $$4B\omega{r}^{2}$$
  • $$\cfrac{B\omega{r}^{2}}{4}$$
A rectangular loop of sides $$a$$ and $$b$$ is placed in $$x-y$$ plane. A uniform but time varying magnetic field of strength $$\vec { B } =20t\hat { i } +10{ t }^{ 2 }\hat { j } +50\hat { k } $$ is present in the region. The magnitude of induced emf in the loop at time $$t$$ is :
  • $$20+20t$$
  • $$20$$
  • $$20t$$
  • zero
A wooden stick of length $$3l$$ is rotated about an end with constant angular velocity $$\omega$$ 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
222693.PNG
  • $$\dfrac{9B\omega {l}^{2}}{2}$$
  • $$\dfrac{4B\omega {l}^{2}}{2}$$
  • $$\dfrac{5B\omega {l}^{2}}{2}$$
  • $$\dfrac{B\omega {l}^{2}}{2}$$
A rod of length $$L$$ rotates in the form of a conical pendulum with an angular velocity $$\omega$$ about its axis as shown in figure. The rod makes an angle $$\theta$$ with the axis. The magnitude of the motional emf developed across the two ends of the rod is
223147.PNG
  • $$\cfrac{1}{2}B\omega {L}^{2}$$
  • $$\cfrac{1}{2}B\omega {L}^{2}\tan ^{ 2 }{ \theta } $$
  • $$\cfrac{1}{2}B\omega {L}^{2}\cos ^{ 2 }{ \theta } $$
  • $$\cfrac{1}{2}B\omega {L}^{2}\sin ^{ 2 }{ \theta } $$
  • answer required
A conducting rod of  length $$0.5 m $$ rotates about a horizontal axis passing through one of its ends and perpendicular to its length with angular velocity of $$4 rad/s$$. A uniform magnetic field of $$2.0T$$ exists parallel to the axis of rotation. The emf developed across the ends of the conductor will be 
  • $$0V$$
  • $$1V$$
  • $$2V$$
  • $$0.5V$$
Two identical conducting rings $$A$$ and $$B$$ of radius $$R$$ are rolling over a horizontal conducting plane with same speed $$v$$ but in opposite direction. A constant magnetic field $$B$$ is present pointing into the plane of the paper. Then the potential difference between the highest points of the two rings is
222979_d3c0d03671df4ff681a829072530c872.png
  • $$0$$
  • $$2BvR$$
  • $$4BvR$$
  • none of these
  • answer required
$$AB$$ is a resistanceless conducting rod which forms a diameter of a conducting ring of radius $$r$$ rotating in a uniform magnetic field $$B$$ as shown in figure. The resistors $${R}_{1}$$ and $${R}_{2}$$ do not rotate. Then the current through the resistor $${R}_{1}$$
223044.PNG
  • $$\cfrac { B\omega { r }^{ 2 } }{ 2{ R }_{ 1 } } $$
  • $$\cfrac { B\omega { r }^{ 2 } }{ 2{ R }_{ 2 } } $$
  • $$\cfrac { B\omega { r }^{ 2 } }{ 2{ R }_{ 1 }{ R }_{ 2 } } \left( { R }_{ 1 }{ +R }_{ 2 } \right) \quad $$
  • $$\cfrac { B\omega { r }^{ 2 } }{ 2\left( { R }_{ 1 }{ +R }_{ 2 } \right) } $$
  • answer required
A circular loop of radius $$r$$, having $$N$$ turns of a wire, is placed in a uniform and constant magnetic field $$B$$. The normal loop makes an angle $$\theta$$ with the magnetic field. Its normal rotates with an angular velocity $$\omega$$ such that the angle $$\theta$$ is constant. Choose the correct statement from the following.
  • emf in the loop is $$NB\omega {r}^{2}/2 \cos{\theta}$$
  • emf induced in the loop is zero
  • emf must be induced as the loop crosses magnetic lines.
  • emf must not be induced as flux does not change with time.
  • answer required
Magnetic flux linked with a stationary loop resistance $$R$$ varies with respect to time during the time period $$T$$ as follows:
$$\phi=at(T-t)$$
The amount of heat generated in the loop during that time (inductance of the coil is negligible) is
  • $$\cfrac{\alpha T}{3R}$$
  • $$\cfrac{{a}^{2}{T}^{2}}{3R}$$
  • $$\cfrac{{a}^{2}{T}^{2}}{R}$$
  • $$\cfrac{{a}^{2}{T}^{3}}{3R}$$
In the figure, there exists a uniform magnetic field $$B$$ into the plane of paper. Wire $$CD$$ is in the shape of an arc and is fixed. $$OA$$ and $$OB$$ are the wires rotating with angular velocity $$\omega$$ as shown in the figure in the same plane as that of the arc about point $$O$$. If at some instant, $$OA=OB=1$$ and each wire makes angle $$\theta={30}^{o}$$ with y-axis, then the current through resistance $$R$$ is (wire $$OA$$ and $$OB$$ have no resistance)
222578.PNG
  • $$0$$
  • $$\cfrac{B\omega {l}^{2}}{R}$$
  • $$\cfrac{B\omega {l}^{2}}{2R}$$
  • $$\cfrac{B\omega {l}^{2}}{4R}$$
  • answer required
The current through the coil in figure (i) varies as shown in figure (ii). Which graph best shows ammeter $$A$$ reading as a function of time?
222559.PNG
  • answer required
A semicircular wire of radius $$R$$ is rotated with constant angular velocity about an axis passing through one end and perpendicular to the plane of the wire. There is a uniform magnetic field of strength $$B$$. The induced emf between the ends is
222836_222b27fbaf9e4896be161d8d159ff076.png
  • $$B\omega {R}^{2}/2$$
  • $$2B\omega {R}^{2}$$
  • is variable
  • none of these
The magnetic flux $$\phi$$ linked with a conducting coil depends on time as $$\phi=4{t}^{n}+6$$, where $$n$$ is a positive constant. The induced emf in the coil is $$e$$.
  • If $$0< n< 1, e\ne 0$$ and $$\left| e \right| $$ decreases with time
  • If $$n=1,e$$ is constant
  • If $$n>1,\left| e \right| $$ increases with time
  • If $$n>1, \left| e \right| $$ decreases with time
  • answer required
A disc of radius $$R$$ is rolling without sliding on a horizontal surface with a velocity of center of mass $$v$$ and angular velocity $$\omega$$ in a uniform magnetic field $$B$$ which is perpendicular to the plane of the disc as shown in figure. $$O$$ is the center of the disc and $$P,Q,R$$ and $$S$$ are the four points on the disc. Which of the following statements is true?
223512.PNG
  • Due to translation, induced emf across $$PS=Bvr$$
  • Due to rotation, induced emf across $$QS=0$$
  • Due to translation, induced emf across $$RO=0$$
  • Due to rotation, induced emf across $$OQ=Bvr$$
The self inductance of a coil having 500 turns is 5 mH. The magnetic flux through the cross - sectional area of the coil while current through it is 8 mA is found to be :
  • $$8\times 10^{-9}Wb$$
  • $$0.8\times 10^{-9}Wb$$
  • $$8\times 10^{-6}Wb$$
  • $$80\times 10^{-3}Wb$$
A long wire carries a steady current of 1 Ampere. A ''S'' shaped conducting rod AB consisting of two semicircles each of radius r is placed in such a way that the centre C of the conducting wire is at a distance 2r from the end of the wire.The rod AB moves with velocity of 5$$ms^{-1}$$ along the direction of the current flow as shown in the figure. If the line joining the ends of the rod makes an angle $$60^{\circ}$$ with the wire then,

265738.png
  • the emf induced between the ends of the rod is (ln 4)$$\mu V$$
  • the end A is at higher potential than end B.
  • the end A is at lower potential than end B.
  • the emf induced between the ends of the rod is (ln 3)$$\mu V.$$
A thin semicircular conducting ring of radius $$R$$ is falling with its plane vertical in horizontal magnetic induction $$\vec { B } $$. At the position $$MNQ$$, the speed of the ring is $$V$$, and the potential difference developed across the ring is
226829_a97689190b0c4793a8e1a4151437c184.png
  • zero
  • $$BV\pi {R}^{2}/2$$ and $$M$$ is at higher potential
  • $$\pi RBV$$ and $$Q$$ is at higher potential
  • $$2RBV$$ and $$Q$$ is at higher potential
The magnetic flux $$ \phi $$ linked with a coil depends on time t as $$ \phi = at^n $$ , where a and n are constants. The emfinduced in the coil is e
  • If 0 < n < 1, e = 0
  • If 0 < n < 1, e $$\neq$$ 0
  • If n = 1, e is constant
  • If n > 1, |e| increases with time
In figure, $$R$$ is a fixed conducting ring of negligible resistance and radius $$a$$. It is hinged at the center of the ring and rotated about this point in clockwise direction with a uniform angular velocity $$\omega$$. There is a uniform magnetic field of strength $$B$$ pointing inward and $$r$$ is a stationary resistance. Then
223503_0766d98c018b4b78b6885dcd39a7dfc4.png
  • current through $$r$$ is zero
  • current through $$r$$ is $$(2B\omega {a}^{2})/5r$$
  • direction of current in external resistance $$r$$ is from center to circumference
  • direction of current in external resistance $$r$$ is from circumference to center
  • answer required
A uniform thin rod of length L is moving in a uniform magnetic field $$\displaystyle B_{0}$$ such that velocity of its centre of mass is v and angular velocity is $$\displaystyle \omega=\frac{4v}{L}$$ Then
332659_1850277e9c2542cca38a6fc93a6134e0.png
  • e.m.f. between end P and Q of the rod is $$\displaystyle B_{0}lv$$
  • end P of the rod is at higher potential than end Q of the rod
  • end Q of the rod is at higher potential than end P of the rod
  • the electrostatic field induced in the rod has same direction at all points along the length of rod
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