You are here:

Welcome to our Physics lesson on **Power and Energy**, this is the fifth lesson of our suite of physics lessons covering the topic of **Induction and Energy Transfers**, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.

Again, we use the outcomes of the analysis made in the previous paragraphs to calculate the rate of work (power) delivered during the process discussed earlier. We have:

P = F_{M} ∙ v

= (*B*^{2} ∙ w^{2} ∙ v*/**R*) ∙ v

=*B*^{2} ∙ w^{2} ∙ v^{2}*/**R*

=*ε*_{i}^{2}*/**R*

= (

=

=

As for the rate of thermal energy produced in the coils, we have:

P = i^{2} ∙ R

= (*B ∙ w ∙ v**/**R*)^{2} ∙ R

=*B*^{2} ∙ w^{2} ∙ v^{2}*/**R*

= (

=

This value is the same as the one obtained earlier for the rate of work done in the coil. This means the work done for pulling the loop through a magnetic field is transferred entirely to the loop in the form of thermal energy.

A 30 cm × 25 cm rectangular loop is pulled at constant speed out a 5.0 T uniform magnetic field as shown in the figure.

It takes 10 seconds to the pulling force to shift the coil out of the magnetic field. If the average resistance provided by the coil during this process is 2.0 Ω, calculate:

- The current induced in the coil
- The average pulling force applied in the coil
- The emf induced in the coil
- The rate at which the external source is doing work on the coil
- The total thermal energy transferred to the coil

Clues:

l = 30 cm = 0.30 m

w = 25 cm = 0.25 m

B = 5.0 T

Δt = 10 s

R = 2.0 Ω

a) i = ?

b) F = ?

c) εi = ?

d) P = ?

e) E = ?

- First, we must calculate the speed of the coil. Since it is moving at constant speed, we have: v =The current induced in the coil due to its motion relative to the magnetic field therefore is
*l**/**∆t*

= (0.30 m)/(10 s)

= 0.03 m/si =*B ∙ w ∙ v**/**R*

=*(5.0 T) ∙ (0.25 m) ∙ (0.03 m/s)**/**(2.0 Ω)*

= 0.01875 A - Since the coil is moving at constant speed, the pulling force F is equal to the resistive magnetic force F
_{m}acting in the coil due to its motion inside the magnetic field. Thus,F = F_{M}= i ∙ B ∙ w

= (0.01875 A) ∙ (5.0 T) ∙ (0.25 m)

= 0.0234 N - The induced emf can be calculated in many ways. One of them is by applying the Ohm's Law. Thus, ε
_{i}= i ∙ R

= (0.01875 A) ∙ (2.0 Ω)

= 0.0375 V - The rate of word done at the coil represents the useful power of the external source. Thus, we have P = F ∙ v

= (0.0234 N) ∙ (0.03 m/s)

= 0.0007 W - The thermal energy can be calculated in many ways. For example, since energy = power × time, we can write E = P ∙ ∆tAnother method for calculating the thermal energy would be

= 0.0007 W ∙ 10 s

= 0.007 JE = (As you see, the result is the same in both methods used.) ∙ ∆t*B*^{2}∙ w^{2}∙ v^{2}*/**R*

=*(5.0 T)*^{2}∙ (0.25 m)^{2}∙ (0.03 m/s)^{2}*/**(2.0 Ω)*__∙ (10 s)__

= 0.007 J

You have reached the end of Physics lesson **16.10.5 Power and Energy**. There are 6 lessons in this physics tutorial covering **Induction and Energy Transfers**, you can access all the lessons from this tutorial below.

Enjoy the "Power and Energy" physics lesson? People who liked the "Induction and Energy Transfers lesson found the following resources useful:

- Energy Feedback. Helps other - Leave a rating for this energy (see below)
- Magnetism Physics tutorial: Induction and Energy Transfers. Read the Induction and Energy Transfers physics tutorial and build your physics knowledge of Magnetism
- Magnetism Revision Notes: Induction and Energy Transfers. Print the notes so you can revise the key points covered in the physics tutorial for Induction and Energy Transfers
- Magnetism Practice Questions: Induction and Energy Transfers. Test and improve your knowledge of Induction and Energy Transfers with example questins and answers
- Check your calculations for Magnetism questions with our excellent Magnetism calculators which contain full equations and calculations clearly displayed line by line. See the Magnetism Calculators by iCalculator™ below.
- Continuing learning magnetism - read our next physics tutorial: Induced Electric Fields

We hope you found this Physics lesson "Induction and Energy Transfers" useful. If you did it would be great if you could spare the time to rate this physics lesson (simply click on the number of stars that match your assessment of this physics learning aide) and/or share on social media, this helps us identify popular tutorials and calculators and expand our free learning resources to support our users around the world have free access to expand their knowledge of physics and other disciplines.

- Angular Frequency Of Oscillations In Rlc Circuit Calculator
- Calculating Magnetic Field Using The Amperes Law
- Capacitive Reactance Calculator
- Current In A Rl Circuit Calculator
- Displacement Current Calculator
- Electric Charge Stored In The Capacitor Of A Rlc Circuit In Damped Oscillations Calculator
- Electric Power In A Ac Circuit Calculator
- Energy Decay As A Function Of Time In Damped Oscillations Calculator
- Energy Density Of Magnetic Field Calculator
- Energy In A Lc Circuit Calculator
- Faradays Law Calculator
- Frequency Of Oscillations In A Lc Circuit Calculator
- Impedance Calculator
- Induced Emf As A Motional Emf Calculator
- Inductive Reactance Calculator
- Lorentz Force Calculator
- Magnetic Dipole Moment Calculator
- Magnetic Field At Centre Of A Current Carrying Loop Calculator
- Magnetic Field In Terms Of Electric Field Change Calculator
- Magnetic Field Inside A Long Stretched Current Carrying Wire Calculator
- Magnetic Field Inside A Solenoid Calculator
- Magnetic Field Inside A Toroid Calculator
- Magnetic Field Produced Around A Long Current Carrying Wire
- Magnetic Flux Calculator
- Magnetic Force Acting On A Moving Charge Inside A Uniform Magnetic Field Calculator
- Magnetic Force Between Two Parallel Current Carrying Wires Calculator
- Magnetic Potential Energy Stored In An Inductor Calculator
- Output Current In A Transformer Calculator
- Phase Constant In A Rlc Circuit Calculator
- Power Factor In A Rlc Circuit Calculator
- Power Induced On A Metal Bar Moving Inside A Magnetic Field Due To An Applied Force Calculator
- Radius Of Trajectory And Period Of A Charge Moving Inside A Uniform Magnetic Field Calculator
- Self Induced Emf Calculator
- Self Inductance Calculator
- Torque Produced By A Rectangular Coil Inside A Uniform Magnetic Field Calculator
- Work Done On A Magnetic Dipole Calculator