NCERT Exemplar Class 12 Physics Solutions Chapter 6 Electromagnetic Induction is a critical chapter for exams. In this chapter, you will learn Faraday's laws, Lenz's law, and how changing magnetic fields induce electric fields. Students will also learn important applications such as transformers and generators.
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NCERT Exemplar Class 12 Physics Solutions Chapter 6 Electromagnetic Induction provides the relationship between electricity and magnetism. It provides the answers of interesting questions such as how electric currents can be generated by moving magnets. The chapter discusses important experiments conducted by scientists to establish the practical applications of this concept. These topics are very crucial for board exams and competitive exams. Students can also download the NCERT Exemplar Class 12 Physics Solutions Chapter 6 PDF for quick reference.
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Question:6.1
A square of side L meters lies in the x-y plane in a region, where the magnetic field is given by $B = B_o (2i + 3j + 4k)T$ where Bo is constant. The magnitude of flux passing through the square is
$(a) 2 B_o L^2 Wb.$
$(b) 3 B_o L^2 Wb.$
$(c) 4 B_o L^2 Wb.$
$(d) \sqrt{}2 9B_o L^2 Wb.$
Answer:
For elementary area dA of a surface, flux linked $d\phi=BdA\cos \theta\:or\: d\phi=\vec{B}.\vec{dA}$Question:6.2
A loop, made of straight edges has six corners at $A(0,0,0), B(L,O,0) C(L,L,0), D(0,L,0) E(0,L,L) \: and\: F(0,0,L)$. A magnetic field B $= B_o (i + k) T$is present in the region. The flux passing through the loop ABCDEFA (in that order) is
$(a) B_o\: L^2 Wb.$
$(b) 2 B_o L^2 Wb.$
$(c) \sqrt{}2 B_o L^2 Wb.$
$(d) 4 \: B_o L^2 Wb.$
Answer:
In this problem first we have to analyse area vector, loop ABCDA lies in x-y plane whose area vector $\vec{A_1}= L^2\hat{k}$ whereas loop ADEFA lies in y-z plane whose area vector $\vec{A_2}= L^2\hat{i}$
And magnetic flux is
$\\ \phi _m=\vec{B}.\vec{A}\\ \vec{A}=\vec{A_1}+\vec{A_2}=\left ( L^2\hat{k} +L^2\hat{i}\right )\\ and\: \vec{B}=B_0\left ( \hat{i}+\hat{k} \right )\\ Now,\phi _m=\vec{B}.\vec{A}= B_0\left ( \hat{i}+\hat{k}\right ).\left ( L^2\hat{k} +L^2\hat{i}\right )\\ =2B_0L^2Wb$
Question:6.3
A cylindrical bar magnet is rotated about its axis. A wire is connected from the axis and is made to touch the cylindrical surface through a contact. Then
(a) a direct current flows in the ammeter A.
(b) no current flows through the ammeter A.
(c) an alternating sinusoidal current flows through the ammeter A with a time period T=2π/ω.
(d) a time-varying non-sinusoidal current flows through the ammeter A.
Answer:
b)Question:6.4
There are two coils A and B as shown in figure. A current starts flowing in B as shown when A is moved towards B and stops when A stops moving. The current in A is counter clockwise. B is kept stationary when A moves. We can infer that
(a) there is a constant current in the clockwise direction in A.
(b) there is a varying current in A.
(c) there is no current in A.
(d) there is a constant current in the counter clockwise direction in A.
Answer:
The answer is the option (d)Question:6.5
Same as problem 4 except the coil A is made to rotate about a vertical axis. No current flows in B if A is at rest. The current in coil A, when the current in B (at t = 0) is counterclockwise and the coil A is as shown at this instant, t = 0, is
(a) constant current clockwise.
(b) varying current clockwise.
(c) varying current counterclockwise.
(d) constant current counterclockwise.
Answer:
The answer is the option (a)Question:6.6
The self-inductance L of a solenoid of length l and area of cross-section A, with a fixed number of turns N increases as
(a) l and A increase.
(b) l decreases and A increases.
(c) l increases and A decreases.
(d) both l and A decrease.
Answer:
The answer is the option (b)$L=\frac{\left ( \mu_ r \: \mu_0\: n^2 \right )}{I}$
So, from the equation, the inductance should increase as l decreases and A increases. As, L is inversely proportional to l and directly proportional to A.
Question:6.7
A metal plate is getting heated. It can be because
(a) a direct current is passing through the plate
(b) it is placed in a time varying magnetic field
(c) it is placed in a space varying magnetic field, but does not vary with time
(d) a current (either direct or alternating) is passing through the plate
Answer:
The correct answers are the options (a,b,c)Question:6.8
An e.m.f is produced in a coil, which is not connected to an external voltage source. This can be due to
(a) the coil being in a time varying magnetic field.
(b) the coil moving in a time varying magnetic field.
(c) the coil moving in a constant magnetic field.
(d) the coil is stationary in external spatially varying magnetic field, which does not change with time.
Answer:
The correct answers are the options (a,b,c)Question:6.9
The mutual inductance M12 of coil 1 with respect to coil 2
(a) increases when they are brought nearer
(b) depends on the current passing through the coils
(c) increases when one of them is rotated about an axis
(d) is the same as M21 of coil 2 with respect to coil 1
Answer:
The correct answers are the options (a, d)
According to Faraday's second law emf induces in secondary $e_2=-N_2\frac{d\phi _2}{dt};e_2=-M\frac{di_1}{dt}$
The mutual inductance M12 of coil 1 wrt coil 2 increases when they are brought nearer and is the same as M21 of coil with respect to coil 1.
M12 e.g. mutual inductance of solenoid S1 with respect to solenoid S2 is given by
$M_{12}= \frac{\mu_0 N_1 N_2 \pi {r_{1}}^{2}}{l}$
Where signs are as usual,
Also, M21, i.e. mutual inductance of solenoid S2 with respect to solenoid S1 is given by:
$M_{21}= \frac{\mu_0 N_1 N_2 \pi {r_{1}}^{2}}{l}$
So we have $M_{12}=M_{21}= M$
Question: 6.10
A circular coil expands radially in a region of magnetic field and no electromotive force is produced in the coil. This can be because
(a) the magnetic field is constant.
(b) the magnetic field is in the same plane as the circular coil and it may or may not vary.
(c) the magnetic field has a perpendicular (to the plane of the coil) component whose magnitude is decreasing suitably.
(d) there is a constant magnetic field in the perpendicular (to the plane of the coil) direction.
Answer:
Answer: The correct answers are the options (b, c)Question:6.11
Answer:
As shown in the figure, the magnet bar and the coil are stationary, therefore there would be no change in the magnetic flux linked to the projected area of the coil. Hence there would be no EMF generate and if there is no EMF, there is not going to be any current flowing in the circuit when it is closed.Question:6.12
Answer:
This solution for this problem can be explained using Lenz’s law. The states that, in a conductor, the direction of induced EMF is such that it opposes it because that produced it. Here if the current-carrying tightly wound solenoid is stretched, the flux would try to leak through the gaps. Therefore, the system will try to oppose this decrease in magnetic flux and hence the current will increase.Question:6.13
Answer:
The iron core, when inserted in the coil, will increase the magnetic field due to the magnetization of the iron bar. So according to Lenz’s law, this increase in the magnetic field should be opposed, therefore, the current will decrease.Question:6.14
Answer:
Here, initially, there was no flux linked to the ring. When a sudden current passes through the solenoid, a magnetic field is induced. This magnetic field is now linked to the ring, so a current would get induced in the ring which would oppose the magnetic field. Hence ring will jump, both the magnetic fields (solenoid and ring induced) will interact.Question:6.15
Answer:
Here, the ring will now experience a downward force. This is followed from the Lenz’s law, as the current stops flowing in the solenoid; the magnetic flux will also get decreases. A current in the ring will be induced so as to oppose that and hence it will experience a downward force.Question:6.16
Answer:
The magnetized cylindrical bar carries a magnetic field with it. So, when it moves inside the metallic bar, the magnet field lines change w.r.t. the metallic hollow cylinder. This change in magnetic flux linked to the metallic pipe is opposed by it. Therefore, a force is applied on the magnetic cylinder; hence it takes more time to travel through the pipe.Question:6.17
A magnetic field in a certain region is given by $B=B_{0}\cos \left ( \omega t \right )$ and a coil of radius a with resistance R is placed in the x-y plane with its centre at the origin in the magnetic field (figure). Find the magnitude and the direction of the current at (a, 0, 0) at
$t=\frac{\pi }{2\omega },t=\frac{\pi }{\omega }\; and\; t=\frac{3\pi }{2\omega }$
Answer:
$\phi _{m}=\vec{B}.\vec{A}=BA\; \cos \theta$Question:6.18
Answer:
The magnetic flux is same as in $S_{1}$ and $S_{2}$ as magnetic field lines do not start anywhere in the space because of continuity. As the numbers of magnetic field lines passing through the circuit are same, therefore the flux would be same for both of them.Question:6.19
Answer:
Question:6.20
Answer:
$\varepsilon =-\frac{d(N\phi _{B})}{dt}$Question:6.21
Answer:
The mutual inductance of coil B with respect to coil A isQuestion:6.22
Answer:
Due to motion : $e=Blv$Question:6.23
A conducting wire XY of mass m and negligible resistance slides smoothly on two parallel conducting wires as shown in figure. The closed circuit has a resistance R due to AC. AB and CD are perfect conductors. There is a magnetic field
(i) Write down an equation for the acceleration of the wire XY
(ii) If B is independent of time, obtain v(t), assuming v(0) = u0
(iii) For (ii), show that the decrease in kinetic energy of XY equals the heat lost in.
Answer:
Upon analyzing the situation:Question:6.24
Answer:
When the conductor OP is rotated, then the rate of change of area and hence the rate of change of flux can be considered uniform fromQuestion:6.25
Answer:
Let us consider a strip of length l and width dr at a distance r from an infinite long current carrying wire. The magnetic field in the strip is given by:Question:6.26
Answer:
$I=\frac{E}{R}=\frac{1}{R}\frac{d\phi }{dt}$Question:6.27
Answer:
The magnetic field decreases which induce an emf hence electric field around the ring. And therefore, the ring experiences a torque which produces a change in angular momentum.Question:6.28
Answer:
The component of magnetic field along the inclined plane will be $=B\sin \theta$ and other will be perpendicular i.e. $=B\cos \theta$. The conductor is moving perpendicular to $=B\cos \theta$. It is the vertical component of the magnetic field. The movement will cause motional emf across the two ends of the rod.Question:6.29
Answer:
Due to the motion of the conductor, motional emf is induced in the conductor. It will give rise to a current.Question:6.30
Answer:
By applying KVL in the given circuit, we haveQuestion:6.31
Answer:
Here a relation is established between the current induced, velocity of free falling ring and power lost. Let the mass of ring be m and radius l;Question:6.32
Answer:
Magnetic field caused by a solenoid is given by1. Faraday's Experiments: Changing magnetic flux through a coil induces an electromotive force (emf).
2. Magnetic Flux $\left(\Phi_B\right)$ : Measure of magnetic field passing through a surface.
3. Lenz's Law: The direction of induced emf opposes the change in magnetic flux (conservation of energy).
4. Motional Electromotive Force: When a conductor moves in a magnetic field, an emf is induced.
5. Eddy Currents: Circular currents induced in conductors due to changing magnetic fields, leading to energy loss.
6. Inductance: The property of a coil to oppose changes in current.
7. AC Generator: Converts mechanical energy into electrical energy using electromagnetic induction.
Chapter 6 Electromagnetic Induction |
Frequently Asked Questions (FAQs)
Yes, this chapter is one of the important parts of the Physics Class 12 syllabus, which will help in scoring well in the board exams.
You can use the NCERT exemplar Class 12 Physics solutions chapter 6 as a reference while solving questions. The solutions are also helpful for knowing the pattern that is the CBSE board exam suitable.
All 32 questions from the exercise of Class 12 Physics NCERT exemplar solutions chapter 6 of the electromagnetic induction chapter is solved in complete and thorough detail.
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