Energy Consideration

In terms of energy considerations, electromagnetic induction can be used to transfer energy from one system to another. For example, a transformer is a device that uses electromagnetic induction to transfer electrical energy from one circuit to another at a different voltage level. In a transformer, an alternating current (AC) flows through a primary coil, which creates a changing magnetic field. This changing magnetic field then induces a current in a secondary coil, transferring energy from the primary circuit to the secondary circuit.

We exert power on our bodies to complete daily tasks; to do this, we need energy. Here, we can see a connection between force and energy, and the energy consideration is what makes this connection possible. By utilizing the idea of energy consideration in motional emf, we may demonstrate that motional emf is right or valid in accordance with the conservation of energy.

What is Consideration Energy?

In the context of electromagnetic induction, consideration energy refers to the energy being transferred from one system to another through the process of electromagnetic induction. This can occur in a variety of situations, such as when a transformer is used to transfer electrical energy from one circuit to another at a different voltage level, or when an electric generator is used to convert mechanical energy into electrical energy.

In general, consideration energy refers to the energy being taken into account or considered in a particular situation or process. This can refer to the energy being transferred, stored, or used in some way. In the case of electromagnetic induction, the consideration energy is the energy being transferred from one system to another through the process of electromagnetic induction.

We may demonstrate that motional emf is accurate or valid in accordance with the conservation of energy by using the notion of energy consideration in motional emf. We are studying the idea of considering energy separately because we will use mathematics to demonstrate the correctness in this case.

Energy Consideration Physics

In physics, energy consideration refers to the process of taking into account the energy involved in a particular situation or process. This can include analyzing the energy being transferred, stored, or used in some way. In the context of electromagnetic induction, energy consideration involves analyzing the energy being transferred from one system to another through the process of electromagnetic induction.

In general, understanding and analyzing energy considerations is important in a wide range of fields, including physics, engineering, and technology. For example, in the field of thermodynamics, energy considerations are important in understanding how heat is transferred between different systems and how work can be performed using thermal energy. In the field of electrical engineering, energy considerations are important in the design and operation of devices such as transformers and generators, which rely on electromagnetic induction to transfer energy.

Overall, energy consideration is an important concept in physics and related fields, and is a fundamental aspect of understanding and analyzing the behaviour of energy in various systems and processes.

Energy Consideration: A Quantitative Study

We will be concentrating on Lenz’s law and the law of energy conservation as we apply the ideas of energy consideration in Motion EMF. Lenz’s Law and the law of conservation of energy are compatible, so bear that in mind. To illustrate this, let’s use the example of a conductor set up as follows:

As indicated in the image below, suppose that a rectangular frame (A) is positioned in a magnetic field (B), If we look at this image, we can see one rod with a length of “l” and the label “CD,” which has a left-to-right velocity of “v.”

It is important to remember that the rod should always be kept perpendicular to the magnetic field, and there is a rationale for doing so as well, which is mentioned below in terms of a mathematical formula.

Consider a conductor that is rectangular in shape. We can infer from the illustration that the rectangular conductor’s sides are AB, CD, BC, and DA. Now, three of the sides of this rectangular conductor are fixed, but one of them, side AB, is free.

Let ‘r’ represent the conductor’s adjustable resistance. As a result, in comparison to this movable resistance, the resistance of the remaining three sides of the rectangular conductor—sides CD, DA, and BC—is very low. If we alter the flux in a magnetic field that is always present, an emf is produced.  

i.e  E = dΦ/dt

We can state that current is present if there is an induced emf E and a moveable resistance r in the conductor, I =  Blv/R. 

As long as there is a magnetic field, there will also be a force F acting since F = ILB. This force, which is determined by force, is directed outward in the direction opposite to the rod’s velocity;

 F = B²l²v/R

Power = force × velocity = B²l²v²/R

The work that is being done in this instance is mechanical, and the mechanical energy is lost as Joule heat. It is stated as P_J = I²R =  B²l²v²/R. 

The mechanical energy then changes into electrical energy and then heat energy. As a result of Faraday’s law, we know that |E| =ΔΦ_B/Δt

Thus, we have, |E| = IR = (ΔQ/Δt)R

As a result, ΔQ=  ΔΦ_B/R.

OR

The definition of electromagnetic induction, states that an induced current is produced in a conductor when there is a changing magnetic field around it. Mathematically, this can be represented as:

ΔΦ = ε

where ΔΦ is the change in the magnetic flux through the conductor (Φ is measured in webers), and ε is the induced electromotive force (measured in volts).

Next, we can use Ohm’s law, which states that the current through a conductor is equal to the voltage across it divided by the resistance of the conductor:

I = V/R

Substituting the expression for ε from the equation above, we get:

I = ΔΦ/R

Finally, we can use the definition of electrical charge, which states that the electrical charge Q is equal to the current multiplied by the time for which it flows:

Q = I × t

Substituting the expression for I from the equation above, we get:

ΔQ = ΔΦB/R

This equation states that the change in electrical charge (ΔQ) is equal to the change in magnetic flux (ΔΦ) divided by the resistance (R) of the conductor. This equation is a useful way to analyze the energy being transferred through the process of electromagnetic induction.

Solved Examples on Energy Consideration

Example 1: In a uniform horizontal magnetic field with a magnitude of 5.0 10^-4 T, a circular loop with a radius of 6.0 m and a circumference of 40 revolves with an angular speed of 45 rad/s about its vertical diameter. if a closed loop of resistance 30 occurs in the coil. Calculate the average power dissipation caused by the Joule heating effect as well as the value of current induced in the coil.

Solution:

Given 
R = 30 , B = 5.0 x 10^-4 T, r = 6 m,  = 45 rad/s, and N = 40

We know that I = e/R and 

e = NωAB 
   = N × πr² × ωB 
   = 40 x 45 x 3.14 x 62x  5.0 × 10^-4
= 1.01736 V 

So, I = 1.01736/10 
        = 0.101736 A

and, Power loss = eI/2 
                          =1.01736 x 0.101736 / 2
                          = 0.052 W.

Example 2: A 0.3 T uniform magnetic field directed normally to an 8 cm by 2 cm rectangular wire loop with a minor cut is travelling out of the region. The loop’s velocity is normal to its longer side, which is 8 cm long. Calculate the emf created across the cut and the duration of the induced voltage.

Solution: 

Given  

A = 8 cm × 2 cm = 16 cm², 
Number of turns in the loop N = 1, 
ω = v/r, where v is the velocity of the loop and the distance travelled by the loop 
r = 8 cm. 

Therefore, the angular velocity of the loop is given by ω = v/r = v/8 cm. The emf generated by the loop is given by 
Emf (E) = NABω 
            = 1 × 0.3 T × 16 cm² × ω.

Let’s say the velocity of the loop is v = 10 cm/s. Then the angular velocity of the loop is given by ω = v/r = 10 cm/s / 8 cm = 1.25 s⁻¹. 

Emf (E) = NABω 
            = 1 × 0.3 T × 16 cm² × 1.25 s⁻¹ 
            = 4 volts. 

The duration of the induced voltage is equal to the time it takes for the loop to travel a distance of 8 cm, which is 

t = r/v 
  = 8 / 10 
  = 0.8 seconds.

If the loop’s velocity is normal to its shorter side, which is 2 cm long, the distance travelled by the loop is

 r = 2 cm and the angular velocity of the loop is given by 

ω = v/r 
    = v/2 .

Duration of the induced voltage is equal to the time it takes for the loop to travel a distance of 2 cm, which is

 t = r/v 
   = 2 / 10 
   = 0.2 seconds.

Example 3: A wire with a resistance of 20 ohms and a length of 2 meters is placed in a uniform magnetic field of strength 1 tesla. The wire is rotated through an angle of 90 degrees in 0.5 seconds. Calculate the heat generated by the wire during this time.

Solution:

Change in flux through the wire is given by ΔΦ = BAcosθ, 

where B is the magnetic field strength, A is the cross-sectional area of the wire, and θ is the angle through which the wire is rotated. 

Since the wire is rotated through an angle of 90 degrees, cosθ = 0 and ΔΦ = 0. 

Therefore, the heat generated by the wire is given by

 ΔQ = ΔΦ_B/R 
       = 0/20 
       = 0 joules.

Example 4: A heater with a resistance of 10 ohms is connected to a 120-volt power supply. Calculate the power dissipated by the heater.

Solution:

Current flowing through the heater is given by Ohm’s law as

i = V/R 
  = 120 
  = 12 amperes. 

Power dissipated by the heater is then given by 

P = i²R

P = 12² × 10 
   = 1440 watts.

FAQs on Energy Consideration

Question 1: Distinguish between the Faraday and Lenz laws.

Answer:

Faraday’s law relates to the electromagnetic force generated, whereas Lenz’s law discusses the conservation of energy applied to electromagnetic induction.

Question 2: What is the primary cause of induced EMF?

Answer:

The fluctuating magnetic flux connected to a current-carrying loop is the underlying cause of induced emf.

Question 3: List some applications of Induced EMF.

Answer:

The following are some examples of real-world uses of induced emf:

• Electric Motor
• Transformers 
• Electric Generators

Question 4: Who formulated Lenz’s Law?

Answer:

Emil Lenz is the author of Lenz’s law. The phenomena of the flow through the circuit are described by this law. This law aids in determining the direction of the current generated by EMI and the induced EMF.

Question 5: What is the significance of energy consideration?

Answer:

A connection between force and energy can be made by considering energy. Energy consideration can also be used to solve Newton’s issues with ease. This is the significance of energy consideration.