Electromagnetic Induction - Quiz 6

Electromagnetic induction : 6

Dear Readers,

JEE Advanced Physics Syllabus can be referred by the IIT aspirants to get a detailed list of all topics that are important in cracking the entrance examination. JEE Advanced syllabus for Physics has been designed in such a way that it offers very practical and application-based learning to further make it easier for students to understand every concept or topic by correlating it with day-to-day experiences. In comparison to the other two subjects, the syllabus of JEE Advanced for physics is developed in such a way so as to test the deep understanding and application of concepts..

Q1.  Switch S of the circuit shown in Fig is closed at t=0

If e denotes the induced e.m.f. in L and i the current flowing through the circuit at time t, then which of the following graphs correctly represents the variation of e with i?

•  
  
•  
  
•  
  
•  
  

Solution
b

Q2.A uniform magnetic field of induction B fills a cylindrical volume of radius R. A rod AB of length 2l is placed as shown in figure. If B is changing at the rate dB/dt, the emf that is produced by the changing magnetic field and that acts between the ends of the rod is

•   dB/dt l√(R²-l² )
•  dB/dt l√(R²+l² )
•  1/2 dB/dt l√(R²-l² )
•  1/2 dB/dt l√(R²+l² )

Solution
a

Q3.  The frequency of oscillation of current in the inductance is

•  1/(3√LC)
•  1/(6π√LC)
•  1/√LC
•  1/(2π√LC)

Solution
b

Q4.  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 filed at point P at a distance r from the centre of the circular region

•  Is zero
•  Decreases as 1/r
•  Increases as r
•  Decreases as 1/r²

Solution
b

Q5.A wire of fixed length is wound on a solenoid of length l and radius r. Its self-inductance is found to be L. Now, if the same wire is wound on a solenoid of length l/2 and radius r/2, then the self-inductance will be

•  2L
•  4L
•  L
•  8L

Solution
 a

Q6. 6. An e.m.f of 15 V is applied in a circuit containing 5 H inductance and 10 Ω resistance. The ratio of the currents at time t=∞ and t=1 s is

•  e^(1/2)/(e^(1/2)-1)
•  e²/(e²-1))
•  1-e^-1
•  e^-1

Solution
b

Q7.Calculate the inductance of a unit length of a double tape line as shown in fig, if the tapes are separated by a distance h which is considerably less than their width b

•  (μ₀ h)/b
•  (μ₀ h)/2b
•  (2μ₀ h)/b
•  (√2 μ₀ h)/bt

Solution
a

Q8. The figure shows certain wire segments joined together to form a coplanar loop. The loop is placed in a perpendicular magnetic field in the direction going into the plane of the figure. The magnitude of the field increases with time. I₁ and I₂ are the currents in the segments ab and cd . Then,

•   I₁>I₂
•  TI₂>I₁
•  I₁is in the direction ba and I₂is in the direction cd
•  I₁is in the direction ab and I₂is in the direction dc

Solution
d

Q9.In fig, the mutual inductance of a coil and a very long straight wire is M, the coil has resistance R and self-inductance L. The current in the wire varies according to the law i=at, where a is a constant and t is the time, the time dependence of current in the coil is

•  M/aR
•  MaRe^-Rt/L
•  M/R e^-tR/L
•  Ma/R(1-e^-tR/L)

Solution
d

Q10. The current generator i_g, shown in figure, sends a constant current i through the circuit. The wire ab has a length l and mass m slide on the smooth, horizontal rails connected to i_g. The entire system lies in a vertical magnetic field B. The velocity of the wire as a function of time is

•  ilBt/m
•  ilBt/2m
•  2ilBt/m
•  ilBt/3m

Solution
a

Dear Readers,

JEE Advanced Physics Syllabus can be referred by the IIT aspirants to get a detailed list of all topics that are important in cracking the entrance examination. JEE Advanced syllabus for Physics has been designed in such a way that it offers very practical and application-based learning to further make it easier for students to understand every concept or topic by correlating it with day-to-day experiences. In comparison to the other two subjects, the syllabus of JEE Advanced for physics is developed in such a way so as to test the deep understanding and application of concepts..

Q1.  Switch S of the circuit shown in Fig is closed at t=0

If e denotes the induced e.m.f. in L and i the current flowing through the circuit at time t, then which of the following graphs correctly represents the variation of e with i?

•  
  
•  
  
•  
  
•  
  

Solution
b

Q2.A uniform magnetic field of induction B fills a cylindrical volume of radius R. A rod AB of length 2l is placed as shown in figure. If B is changing at the rate dB/dt, the emf that is produced by the changing magnetic field and that acts between the ends of the rod is

•   dB/dt l√(R²-l² )
•  dB/dt l√(R²+l² )
•  1/2 dB/dt l√(R²-l² )
•  1/2 dB/dt l√(R²+l² )

Solution
a

Q3.  The frequency of oscillation of current in the inductance is

•  1/(3√LC)
•  1/(6π√LC)
•  1/√LC
•  1/(2π√LC)

Solution
b

Q4.  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 filed at point P at a distance r from the centre of the circular region

•  Is zero
•  Decreases as 1/r
•  Increases as r
•  Decreases as 1/r²

Solution
b

Q5.A wire of fixed length is wound on a solenoid of length l and radius r. Its self-inductance is found to be L. Now, if the same wire is wound on a solenoid of length l/2 and radius r/2, then the self-inductance will be

•  2L
•  4L
•  L
•  8L

Solution
 a

Q6. 6. An e.m.f of 15 V is applied in a circuit containing 5 H inductance and 10 Ω resistance. The ratio of the currents at time t=∞ and t=1 s is

•  e^(1/2)/(e^(1/2)-1)
•  e²/(e²-1))
•  1-e^-1
•  e^-1

Solution
b

Q7.Calculate the inductance of a unit length of a double tape line as shown in fig, if the tapes are separated by a distance h which is considerably less than their width b

•  (μ₀ h)/b
•  (μ₀ h)/2b
•  (2μ₀ h)/b
•  (√2 μ₀ h)/bt

Solution
a

Q8. The figure shows certain wire segments joined together to form a coplanar loop. The loop is placed in a perpendicular magnetic field in the direction going into the plane of the figure. The magnitude of the field increases with time. I₁ and I₂ are the currents in the segments ab and cd . Then,

•   I₁>I₂
•  TI₂>I₁
•  I₁is in the direction ba and I₂is in the direction cd
•  I₁is in the direction ab and I₂is in the direction dc

Solution
d

Q9.In fig, the mutual inductance of a coil and a very long straight wire is M, the coil has resistance R and self-inductance L. The current in the wire varies according to the law i=at, where a is a constant and t is the time, the time dependence of current in the coil is

•  M/aR
•  MaRe^-Rt/L
•  M/R e^-tR/L
•  Ma/R(1-e^-tR/L)

Solution
d

Q10. The current generator i_g, shown in figure, sends a constant current i through the circuit. The wire ab has a length l and mass m slide on the smooth, horizontal rails connected to i_g. The entire system lies in a vertical magnetic field B. The velocity of the wire as a function of time is

•  ilBt/m
•  ilBt/2m
•  2ilBt/m
•  ilBt/3m

Solution
a