Electromagnetic Induction

Step 1: Understanding the Concept:
Lenz's law states that the direction of the induced electromotive force (e.m.f.) and hence the induced current in a closed circuit is such that it opposes the change in magnetic flux that produced it. This principle is directly linked to the law of conservation of energy.
Step 2: Detailed Explanation:
Let's consider an example: moving the north pole of a bar magnet towards a closed coil.
1. As the north pole approaches the coil, the magnetic flux through the coil increases.
2. According to Lenz's law, an e.m.f. and current will be induced in the coil in a direction that opposes this increase in flux. To oppose the approaching north pole, the face of the coil towards the magnet must become a north pole itself (like poles repel).
3. This induced north pole creates a repulsive force on the approaching magnet. To keep the magnet moving towards the coil, we must do mechanical work against this repulsive force.
4. This mechanical work done by the external agent is converted into electrical energy in the coil, which manifests as the induced current and can dissipate as heat ( ).
What if Lenz's Law was violated?
Suppose the induced current supported the change instead of opposing it. In our example, the coil would form a south pole. This south pole would attract the approaching north pole, pulling it in faster. This would induce an even larger current, creating a stronger attraction, and so on. This would lead to a self-sustaining increase in kinetic and electrical energy without any external work being done, which would be a clear violation of the law of conservation of energy.
Step 3: Final Answer:
Thus, the very opposition described by Lenz's law necessitates the input of energy (usually mechanical) to produce electrical energy, thereby upholding the principle of conservation of energy.

Step 1: Understanding the Concept:
A current-carrying inductor stores energy in the magnetic field within it. Magnetic energy density ( ) is the amount of this stored energy per unit volume.
Step 2: Key Formula or Approach:
The total energy ( ) stored in an inductor of inductance carrying a current is .
For an ideal long solenoid, the inductance is and the magnetic field inside is , where is the number of turns per unit length, is the cross-sectional area, and is the length. The volume of the solenoid is .
The energy density is .
Step 3: Detailed Explanation:
From the magnetic field formula, we can express the current as .
Now substitute the expressions for and into the energy formula: Cancel out terms ( and one ): The energy density is the energy divided by the volume : Step 4: Final Answer:
The formula for magnetic energy density inside a solenoid (and for any magnetic field in free space) is . Option (A) is correct.

Step 1: Understanding the Concept:
According to Faraday's law of induction and Lenz's law, when the current through an inductor changes, a back electromotive force (emf) is induced across it. This self-induced emf opposes the change in current.
Step 2: Key Formula or Approach:
The self-induced emf ( ) in an inductor is given by the formula: where:
is the self-inductance of the coil.
is the rate of change of current.
The negative sign indicates that the induced emf opposes the change in current (Lenz's Law).
Step 3: Detailed Explanation:
Given values are:
Self-inductance, H.
Rate of increase of current, A/s.
Substitute these values into the formula: Step 4: Final Answer:
The self-induced emf in the choke coil is -10 V. The negative sign signifies that the emf is induced in a direction that opposes the increase in current. Therefore, option (C) is the correct answer.

Step 1: Understanding electromagnetic induction.
Electromagnetic induction refers to the process of generating an electromotive force (EMF) by changing the magnetic field within a conductor. This principle is applied in devices like electric generators.
Step 2: Explanation of options.
- (A) Voltmeter: A voltmeter measures the potential difference between two points but does not operate based on electromagnetic induction.
- (B) Electric motor: An electric motor uses magnetic fields to generate motion, but it does not work based on electromagnetic induction; instead, it works on the force created by current in a magnetic field.
- (C) Electric generator: This device generates electricity based on the principle of electromagnetic induction, as it converts mechanical energy into electrical energy by rotating a coil in a magnetic field.
- (D) Ammeter: An ammeter measures the current flowing through a circuit and does not operate based on electromagnetic induction.
Step 3: Conclusion.
An electric generator works based on electromagnetic induction, making it the correct choice.