PhysicsKund Physics class 9 to 12 NCERT, JEE - NEET

Lenz's Law The polarity of induced e.m.f in a closed circuit or coil is such that it oppose the cause which produces it. Faraday 's law of electromagnetic induction, induced e.m.f. in a closed circuit is given by :  $E= -N \frac{d\Phi_B}{dt}$ Where:  * \mathcal{E} is the induced EMF  * N is the number of turns in the coil  * \frac{d\Phi_B}{dt} is the rate of change of magnetic flux through the coil * Negative sign shows that induced e.m.f opposes the rate of change of magnetic flux in a closed circuit. Conservation of Energy Energy cannot be created or destroyed, but it can be transformed from one form to another within a closed system. The total amount of energy in an isolated system remains constant over time. The Relationship Between Lenz's Law and Conservation of Energy :  Consider a bar magnet moving towards a coil of wire.As the magnet approaches, the magnetic flux through the coil increases. According to Lenz's Law, the induced current in the coil will cr...

Mutual Inductance of Two Long Co-axial Solenoids of Equal Length Consider two solenoids $S_1$ and $S_2$ such that the solenoid $S_2$ completely surrounds the solenoid $S_1$. Let length of each solenoid be $l$, and the area of cross-section of each solenoid is $A$. Let $N_1$ and $N_2$ be the total number of turns of solenoid $S_1$ and $S_2$ respectively. $\therefore$ Number of turns per unit length of solenoid $S_1$ is given by, $n_1 = \frac{N_1}{l}$. Number of turns per unit length of solenoid $S_2$ is given by, $n_2 = \frac{N_2}{l}$. Let current $I_1$ flow through solenoid $S_1$. Then magnetic field inside the solenoid $S_1$ is given by, $ B_1 = \mu_0 n_1 I_1 = \mu_0 \frac{N_1}{l} I_1 $ Magnetic flux linked with each turn of solenoid $S_2$ is given by,  $d\phi_2 = B_1 A = \mu_0 \frac{N_1}{l} I_1 A$. Then, total magnetic flux linked with $N_2$ turns of the solenoid $S_2$ is given by $ \phi_2 = N_2 d\phi_2$ $ \phi_2= N_2 \mu_0 \frac{N_1}{l} I_1 A$ $ \phi_2= \mu_0 \frac{N_1 N_2}{l} A...

Coefficient of Mutual Induction or Mutual Inductance :  It is known that the magnetic flux linked with the secondary coil is directly proportional to the current flowing through the primary coil. i.e., $\phi_s \propto I_p$ or, $\phi_s = MI_p \quad \dots (1) $ where $M$ is a constant of proportionality called \textbf{co-efficient of mutual induction or Mutual inductance}. If $I_p = 1$, then $M = \phi_s$. Thus, magnetic inductance of two coils or circuits is defined as the magnetic flux linked with the secondary coil due to the flow of unit current in the primary coil. According to Faraday's law of electromagnetic induction, $ \varepsilon_s = - \frac{d\phi_s}{dt} $ Using equation (1), we get $ \varepsilon_s = - \frac{dMI_p}{dt}$ $ \varepsilon_s= -M \frac{dI_p}{dt} \quad \dots (3) $ or $ M = - \frac{\varepsilon_s}{\frac{dI_p}{dt}} \quad \dots (4) $ If $-\frac{dI_p}{dt} = 1$, then $M =\varepsilon_s$. Thus, mutual inductance of two coils can be defined as the induced e.m.f. produced in ...

Derive an expression for self inductance of a solenoid. What happens to the self inductance of the coil if it is wound on a rod of magnetic material. State the factors on which the self inductance of a coil depends. Consider a long solenoid of length $l$, area of cross section $A$ and number of turns per unit length $n$. Let $I$ be the current flowing through the solenoid. The magnetic field inside this solenoid is uniform and given by $ B = \mu_0 n I $ Total number of turns in the solenoid, $N = nl$. Now the magnetic flux linked with each turn of the solenoid, $d\phi_B = B \times A = \mu_0 n I A$. Total magnetic flux linked with the whole solenoid, $ \phi_B = \text{magnetic flux linked with each turn} \times \text{number of turns in the solenoid} $ $ \phi_B = (\mu_0 n I A) \times (nl) = \mu_0 n^2 I Al \quad \dots (1) $ or $ \phi_B = LI \quad \dots (2) $ Also, From (1) and (2), we get $ LI = \mu_0 n^2 I Al $ or $ L = \mu_0 n^2 Al \quad \dots (3) $ Since $n = \frac{N}{l}$. Hence eqn. (3...

Definition of Inductance: Inductance is a fundamental property of an electrical conductor or circuit. It describes the tendency of the conductor to oppose any change in the electric current flowing through it. When the current flowing through a conductor changes, it creates a changing magnetic field around it. According to Faraday's Law of Induction and Lenz's Law, this changing magnetic field induces a voltage (electromotive force or EMF) across the conductor. This induced voltage acts in a direction that opposes the original change in current. In simpler terms: Inductance is like electrical inertia – it resists changes in current flow, just as mass resists changes in velocity. Quantitatively: It is defined as the ratio of the induced voltage (EMF) to the rate of change of current causing it:      E = -L (dI/dt)      Where:      E = induced voltage (EMF)      L = inductance      dI/dt = rate of change of current...

Define Self Inductance and Expression for Coefficient of It. Define Self Inductance :  Self-inductance is the property of a coil (or any conductor) to oppose a change in the current flowing through it by inducing an electromotive force (EMF) in itself.  This phenomenon arises due to Faraday's law of electromagnetic induction. When the current through the coil changes, the magnetic flux linked with the coil also changes, inducing an EMF that opposes this change in current. This induced EMF is also known as back EMF. Self inductance is also knowns as inertia of electricity. Coefficient of Self Induction or Self Inductance :  The magnetic field at any point due to a current carrying coil is directly proportional to the current. Therefore, the magnetic flux ($\phi_B = BA$) through the area bounded by the current carrying coil is directly proportional to the current flowing in the coil, i.e., $ \phi_B \propto I $ $ \phi_B = LI $ where $L$ is the constant of proportionality and...

Chapter 6: Electromagnetic Induction - Physics Kund 1. Electromagnetic Induction: Experiments of Faraday and Henry 2. Magnetic Flux 3. Faraday's Laws of Electromagnetic Induction 4. Lenz's Law and Conservation of Energy 5. Motional Electromotive Force (EMF) 6. Inductance: SI Unit and Dimensions 7. Define Self Inductance and Expression for the Coefficient of Self Inductance 8. Expression for Self Inductance of a Solenoid 9. Energy Stored in an Inductor 10. Expression for the Coefficient of Mutual Induction (Mutual Inductance) 11. Expression for Mutual Inductance of Two Long Co-axial Solenoids 12. AC Generator

Energy Stored In an Inductor  Derive an expression for energy stored in an inductor. In what form, the energy is stored in the inductor? Consider an inductor of inductance $L$ connected across a battery. When current $I$ flows through the inductor, an e.m.f. $\varepsilon$ is induced (called back e.m.f.) in it. This induced e.m.f. is given by, $\varepsilon = -L \frac{dI}{dt} \quad \dots (i)$ -ve sign shows that '$\varepsilon$' opposes the passage of current $I$ in the inductor. To drive the current through the inductor against the induced e.m.f. '$\varepsilon$', the external voltage is applied. Here, external voltage is e.m.f. of the battery $= -\varepsilon$. Hence from eqn. (i) we get,  $\varepsilon = L \frac{dI}{dt} \dots(ii)$ Let an infinitesimal charge $dq$ be driven through the inductor. So the work done by the external supply is given by. $dW= \varepsilon dq$ $dW= L \frac{dI}{dt}dq$ $dW= L dI \frac{dq}{dt}$ $dW = L I dI \quad \left( \because \frac{dq}{dt} = I \righ...

What is Motional Electromotive Force e.m.f.? Derive an expression for it. Definition :  The induced e.m.f. produced due to the motion of a conductor through a uniform magnetic field is called motional e.m.f. Expression : Consider a closed circuit or loop PQRS placed in a uniform magnetic field $\vec{B}$ perpendicular to the plane of the paper and directed into the page (shown by $\otimes$). Let $x$ be the length and $l$ be the breadth of the loop PQRS. The arm RS of the loop is free to move on rails, PS and QR without any friction and let it moves with constant velocity $\vec{v}$ towards the left side. The magnetic flux linked with the loop PQRS is given by $$\phi_B = BA$$ $$(\because A = lx)$$ $$\phi_B= Blx \tag{i}$$ This magnetic flux changes with time. When arm RS moves to left side with velocity $v$, area enclosed by the loop PQRS decreases. According to Faraday's law, induced e.m.f. in the circuit is given by $$ \varepsilon= -\frac{d\phi_B}{dt}$$ $$\varepsilon= -\frac{d}{dt}(B...

State and explain Faraday's Laws of electromagnetic induction. On the basis of his experiments, Faraday stated the laws of electromagnetic induction as given below : (i) Faraday's First Law of Electromagnetic Induction (Qualitative Law) : Whenever magnetic flux linked with a closed conductor (or coil) changes, an e.m.f. is induced in it. This induced e.m.f. lasts so long as the change in magnetic flux continues in the coil. (ii) Faraday's Second Law of electromagnetic induction (Quantitative Law) : The magnitude of the induced e.m.f. in a closed conductor or a coil is directly proportional to the rate of change of magnetic flux linked with the conductor (or coil). Expression for Induced e.m.f. Let $\phi_1$ be magnetic flux linked with a closed circuit or coil at time $t_1$ and $\phi_2$ be magnetic flux linked with a closed circuit or coil at time $t_2$. Then change in magnetic flux in the time interval $(t_2 - t_1) = (\phi_2 - \phi_1)$ Induced e.m.f. $\varepsilon \propto \f...

Define magnetic flux. Give units and dimensions of magnetic flux. Give an expression for magnetic flux associated with variable magnetic field. Magnetic flux ($\phi$) through any surface is defined as " the total number of magnetic lines passing through that surface." Consider a small surface of area A. Let $\hat{n}$ be the unit vector which is drawn normal to the plane of the surface. If $\theta$ is the angle between $\hat{n}$ and the uniform magnetic field $\vec{B}$ , then the magnetic flux ($\phi$) through the surface is given by, $\phi_B = \vec{B} \cdot \vec{A} = BA \cos\theta \tag{i}$ or  $\phi_B = (B \cos\theta) A \tag{ii}$ Now $B \cos \theta$ is the component of the magnetic field normal to the plane of the surface Then eqn. (ii) can be written as,  $\Phi_B = BA \tag{iii}$ Thus, magnetic flux through a given surface is defined as the product of the area of the surface and the component of the magnetic field ($B$) normal to the plane of the surface. Special Cases : (i) ...

Explain Various Experiments performed by Faraday and Henry - Physicskund  Experiment 1 : Relative motion between a bar magnet and a conducting coil induces electric current in the conducting coil. Observations : it was observed that: (i) When the bar magnet was at rest, the galvanometer showed no deflection. (ii) When the bar magnet with its North pole facing the coil moved towards the coil, the galvanometer showed deflection, indicating flow of current in the coil. (iii) When the bar magnet with its North pole facing the coil moved away from the coil, the galvanometer again showed the deflection but now in the opposite direction, indicating flow of current in the coil but in the opposite direction. (iv) The deflection of the galvanometer was large, when the bar magnet was moved faster towards or away from the coil. (v) When the bar magnet with its South pole facing the coil was brought near the coil, or was moved away from the coil, the galvanometer showed deflection in the oppos...