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Chapter 29: Problem 57

Two flat horizontal coils are mounted as shown. Which one of the following actions will not cause the sensitive galvanometer \(G\) to deflect? (a) Coils stationary and coil 1 moves upwards with \(K_{1}\) and \(K_{2}\) closed (b) Both coils stationary, \(K_{2}\) closed and \(K_{1}\) switched on or off (c) With \(K_{1}\) and \(K_{2}\) closed, a variable resistance \(R\) is increased and decreased rapidly (d) Both coils stationary, \(K_{1}\) closed and \(K_{2}\) switched on or off

Short Answer

Expert verified
(d) Both coils stationary, \(K_{1}\) closed and \(K_{2}\) switched on or off.

Step by step solution

01

Understanding Electromagnetic Induction

The galvanometer detects current induced by a change in magnetic flux through the coils. The key concept is Faraday's Law of Electromagnetic Induction, stating that an electromotive force (emf) is induced when there is a change in the magnetic flux through a coil.
02

Analyzing Option (a)

In option (a), coil 1 moves upwards. This movement changes the distance between coil 1 and coil 2, altering the magnetic flux linkage between them since both switches are closed, which will cause a deflection in the galvanometer.
03

Analyzing Option (b)

In option (b), closing switch \(K_{2}\) and switching \(K_{1}\) on or off introduces and removes current flow in coil 1, changing the magnetic field around coil 2. This change alters the magnetic flux in coil 2, causing a galvanometer deflection.
04

Analyzing Option (c)

In option (c), with both switches closed, the variable resistance \(R\) changes the total circuit current. Rapid increase or decrease of \(R\) alters the current flow, changing the magnetic flux linkage in both coils, which results in galvanometer deflection.
05

Analyzing Option (d)

In option (d), with \(K_{1}\) closed and stationary coils, switching \(K_{2}\) on or off also initiates or halts current in coil 2, changing the magnetic field. However, the flux linkage with coil 1 is not affected because coil 1's switch \(K_{1}\) is the primary that creates the stationary magnetic field, thus potentially not affecting the galvanometer.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Faraday's Law
Faraday's Law of Electromagnetic Induction is a fundamental principle used to understand how electrical energy can be generated from magnetic fields. It states that an electromotive force (emf) is induced in a conductor whenever there is a change in magnetic flux surrounding it.

To put it simply, whenever the magnetic environment of a coil changes, it creates a potential difference (or voltage) across the coil.
  • This can happen through the movement of the coil in a magnetic field.
  • Or, by changing the intensity of the magnetic field around the coil.
  • Or, by altering the relative orientation of the coil within the field.
Faraday's Law is the foundational principle explaining how generators and transformers work, helping in converting mechanical energy into electrical energy and vice versa.
Magnetic Flux
Magnetic flux is the measure of the total magnetic field passing through a given coil or surface area. It plays a crucial role in Faraday鈥檚 Law of Induction as it determines the induced emf. Magnetic flux is represented by the Greek letter \( \Phi \) and is calculated using the formula: \[ \Phi = B \cdot A \cdot \cos(\theta) \]where:
  • \(B\) is the magnetic field strength,
  • \(A\) is the area the magnetic field passes through,
  • \(\theta\) is the angle between the magnetic field direction and the perpendicular to the surface.
The concept of magnetic flux helps understand how changes in the magnetic environment lead to induced currents in a conductor. When magnetic flux through a coil changes, it leads to the generation of emf, causing current to flow if the circuit is closed.
Galvanometer Deflection
A galvanometer is an instrument used to detect and measure small amounts of electric current. When connected to a coil, it can show deflection to indicate the presence of an induced current. This deflection is an indicator that electromagnetic induction has occurred due to a change in magnetic flux.

Here鈥檚 how it works in a simple sense:
  • If there is a change in magnetic flux, an emf is induced in the coil.
  • This induced emf leads to a current flow through the coil.
  • The galvanometer then detects this current and deflects accordingly.
The greater the change in flux, the larger the deflection, giving insights into the intensity of the electromagnetic induction taking place.
Induced EMF
Induced EMF, or electromotive force, occurs when there is a change in magnetic flux through a wire or coil. It's the underlying principle of many electrical devices and can be calculated using Faraday's Law.

Induced EMF is all about how rapidly or effectively the magnetic flux changes:
  • If the change in the magnetic environment is quick, the induced EMF is higher.
  • If the change is slow, the induced EMF is lower.
  • The direction of the induced EMF is determined by Lenz's Law, which states that induced current will oppose the change in flux causing it.
Induced EMF is essential for explaining how devices like transformers, electric generators, and motors operate, where changes in magnetic fields initiate currents to perform electrical work.

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Most popular questions from this chapter

Two straight super-conducting rails form an angle \(\theta\) where their ends are joined a conducting bar having \(R_{0}\) resistance per unit length in contact with the rails and forming an isosceles triangle with them. The bar starts at the vertex at time \(t=0\) and moves with constant velocity \(v\) to right. A magnetic field \(B\) is present into the region (shown in figure). Find the force exerted by external agent to maintain constant velocity to the rod: (a) \(\frac{2 B^{2} v^{2} t}{R_{0}} \tan \frac{\theta}{2}\) (b) \(\frac{B^{2} v^{2} t}{R_{0}} \tan \frac{\theta}{2}\) (c) \(\frac{B^{2} v^{2} t}{R_{0}}\) (d) none of these

The self inductance of the air cored solenoid of length \(80 \mathrm{~cm}\) and has 500 turns and its circular cross-section has diameter of \(2 \mathrm{~cm}\) is : (a) \(150.6 \mu \mathrm{H}\) (b) \(162.2 \mu \mathrm{H}\) (c) \(123.3 \mu \mathrm{H}\) (d) \(102.5 \mu \mathrm{H}\)

A fan blade of length \(1 / \sqrt{\pi}\) meter rotates with frequency 5 cycle per second perpendicular to a magnetic field 10 tesla. What is potential difference between the centre and the end of blade ? (a) \(-50 \mathrm{~V}\) (b) \(+50 \mathrm{~V}\) (c) \(-2.0 \mathrm{~V}\) (d) \(+0.02 \mathrm{~V}\)

The perfect formula used for calculating induced emf in a rod moving in a uniform magnetic field is: (a) \(e=\overrightarrow{\mathbf{B}} \cdot(\overrightarrow{\overrightarrow{1}} \times \overrightarrow{\mathbf{v}})\) (b) \(c=\overrightarrow{\mathrm{B}} \cdot(\overrightarrow{1} \cdot \overrightarrow{\mathrm{v}})\) (c) \(e-\overrightarrow{\mathrm{B}} \times(\overrightarrow{1} \cdot \overrightarrow{\mathrm{v}})\) (d) \(e=\overrightarrow{\mathrm{B}} \times(\overrightarrow{1} \times \overrightarrow{\mathrm{v}})\)

A closed circuit consists of a source of \(\operatorname{emf} E\) and an inductor coil of inductance \(L\), connected in series. The active resistance of whole circuit is \(R\). At the moment \(t=0\), inductance of coil abruptly decreased to \(L / n\). Then current in the circuit immediately after, is : (a) zero (b) \(E / R\) (c) \(\frac{n E}{R}\) (d) \(\frac{E}{n R}\)
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