Why Energy Consideration Matters in Solving Physics Problems
We know that force is the push or pull of an object and performing a day-to-day task we apply force on our bodies. For exerting our body, we need energy. So, here can find a link between the force and the energy. Also, the thing that provides a link between these two quantities is the energy consideration.
Through the concept of energy consideration in motional emf, we can prove that motional emf is correct or valid according to the conservation of energy. Here, we are going to prove the validity through mathematical derivation, that’s why we are discussing the concept of consideration of energy individually.
Energy Consideration Physics
In this article, we are going to discuss energy consideration of motional emf and illustrative energy consideration example of a loop.
While applying the principles of energy consideration in Motion EMF, we will be focusing on two important concepts viz: Lenz’s law and the law of energy conservation.
One must keep in mind that Lenz’s Law agrees with the law of conservation of energy and to make it understandable, we are taking a conductor placed in the following manner:
Let’s suppose that there is a rectangular frame placed in a magnetic field (B), as shown in the figure below:
If we observe this figure, there is one rod of length ‘L’ labeled as PQ, which can move left-to-right with a velocity ‘v’.
One must note that the rod should be kept in a direction perpendicular to the magnetic field and the reason for keeping it perpendicular to B also has a significance, which we will understand in terms of mathematical expression later.
Consideration Energy Physics
If we observe the conductor PQ in Fig.1, PQ is a movable arm, and its length is ‘L’, and it is allowed to move with a velocity ‘v’, and the current flowing through this conductor is I. Also, these three quantities viz: L, I, v are perpendicular to each other. Also, the magnetic field marked by ‘x’ is perpendicular to the plane of the sheet on which it is kept and is directed inwards.
We must also consider one more parameter, i.e., the resistance ‘R’. The resistance for PQ is ‘R’ itself, while for QR, RS, and SP, it will be negligible.
So, now the question arises when this conductor PQ starts moving towards the left with a constant velocity, what will be the induced emf generated in this frame? The answer is pretty simple, it will be:
e = BvL….(1)
Now, if wish to find the direction of induced current, we can find out by using Lenz’s law:
From Fig.1, we can see that the rod is moving towards the left and the magnetic field is directed inwards, so the flux is decreasing. As the flux is decreasing, we need to strengthen the magnetic field by adding one more magnetic field pointing downwards. Further, the direction of the current should always be clockwise.
Now, when the current induces in the clockwise direction, it will oppose the decreasing flux.
We must also note that the polarity of EMF at Point P is negative and positive at point Q.
If we are given with induced emf, to ascertain the induced current, we can use Ohm’s law, which is:
I = e/R…….(2)
(Since the resistance is along PQ only)
From eq (1) in (2), we get the current:
I = vBL/R…..(3)
From equation (3), we can say that PQ is a current-carrying conductor with current vBL/R.
The magnetic force on this rod is:
FM = IBL….(4)
= I (B→ x L→) = IBL Sin⊖ = IBL Sin 90 degrees = IBL
From eq (3) in (4):
FM = vB2L2/R……(5)
Here, the direction of the magnetic force or (B x L) is outwards by the Right-hand rule. So, when we are pushing the rod inwards, the flux is decreasing, we immediately apply the magnetic force outwards to oppose the changing flux. Now, this force won’t allow the further inward movement of the rod.
If we still wish to move this rod inwards with a constant velocity, we need an additional force viz: FEXT. So, as the rod moves, FM will counterbalance the effect of FEXT, and therefore, FM and FEXT will become equal and opposite.
To make the rod move inwards with velocity v ultimately by FEXT , we will supply the power by an external agent, which is:
PEXT = FEXT X v…..(6)
Since FEXT = FM, now, from eq (6) in eq (5),we get:
PEXT = FM X v = v2B2L2/R….(7)
Now, if we wish to calculate the power dissipated in the loop PQRs, it is:
PDISS = I2R =(vBL/R)2 * R =v2B2L2/R….(8)
We can observe that power supplied by an external agent = power dissipated in the loop. It means, whatever amount of work is done by us in moving the rod inwards will always get dissipated in the form of heat.
This principle is correct according to the conservation of energy, the work done on the system = energy generated in the system.
Hence, we proved that the motional emf is valid according to the conservation of energy.
FAQs on Energy Consideration in Physics
1. What are energy considerations in the context of electromagnetic induction as per the CBSE Class 12 syllabus?
Energy considerations in electromagnetic induction refer to the application of the Law of Conservation of Energy to explain how electrical energy is produced. When a conductor moves through a magnetic field, or the flux through a circuit changes, an electromotive force (EMF) is induced. The energy for the resulting current doesn't appear from nowhere; it comes from the mechanical work done to move the conductor against the opposing magnetic force, as explained by Lenz's Law. This topic focuses on the transformation of mechanical energy into electrical energy.
2. What is the fundamental cause of an induced EMF according to Faraday's laws?
The fundamental cause of an induced EMF is a change in the magnetic flux linked with a closed circuit or coil. Magnetic flux is the measure of the total magnetic field lines passing through a given area. An EMF is induced, and hence a current flows, as long as this flux is continuously changing. This can be achieved by changing the magnetic field strength, the area of the coil within the field, or the orientation of the coil with respect to the field.
3. How does Lenz's Law demonstrate the principle of conservation of energy?
Lenz's Law is a direct consequence of the principle of conservation of energy. It states that the direction of the induced current is always such that it opposes the very change in magnetic flux that produced it. If the induced current supported the change, it would create a bigger change, inducing an even larger current in a self-perpetuating cycle, creating energy from nothing. Instead, to maintain the induced current, mechanical work must be done against this opposing force. This external work is precisely what gets converted into the electrical energy dissipated in the circuit, thus conserving the total energy of the system.
4. What is the source of the electrical energy produced by an induced current in a generator?
The source of electrical energy in a generator is the mechanical energy used to rotate the coil within the magnetic field. As the coil rotates, the magnetic flux through it changes, inducing a current. According to Lenz's law, this induced current creates a magnetic field that opposes the rotation. Therefore, an external agent (like a turbine driven by wind, water, or steam) must continuously supply mechanical energy to overcome this magnetic drag and keep the coil rotating. This input mechanical work is converted into output electrical energy.
5. What are eddy currents and how do they represent an energy loss?
Eddy currents are loops of electrical current induced within bulk conductors when the magnetic flux passing through them changes. These currents flow in closed loops in planes perpendicular to the magnetic field. As they flow through the resistive material of the conductor, they dissipate energy in the form of heat (Joule heating). This conversion of electrical energy into unwanted heat is an energy loss, which can reduce the efficiency of devices like transformers and electric motors.
6. How can the energy loss due to eddy currents be minimised in practical applications?
Energy loss from eddy currents can be minimised by interrupting their path. Since eddy currents flow in bulk conductors, replacing the solid metallic core with a laminated core is the most common solution. A laminated core is made of thin sheets of metal that are electrically insulated from each other. This design restricts the eddy currents to within each thin lamination, significantly reducing their magnitude and the associated heat loss, thereby increasing the device's efficiency.
7. What are some important real-world applications where energy considerations in electromagnetism are crucial?
Understanding energy transformations in electromagnetism is vital for designing and optimising many devices. Key examples include:
Electric Generators: They are a prime example of converting mechanical energy into electrical energy based on electromagnetic induction.
Transformers: Their efficiency depends on minimising energy losses, primarily through heat from eddy currents and winding resistance.
Induction Cooktops: They use changing magnetic fields to induce eddy currents directly in the metallic cookware, using the resulting heat for cooking.
Electromagnetic Brakes (in trains): They use eddy currents to create a drag force, converting the train's kinetic energy into heat to slow it down without physical friction.
