energy stored in inductor In the figure below, you see a solenoid which has radius \( R \), height \( h \), \( N \) number of turns, and \( n \) number of turns per unit length. Consider its height to be much larger than its radius, so that we can assume the magnetic field to be uniform inside the solenoid and zero outside it, when a current \( I \) is flowing through the coils.![Diagram of a solenoid with radius R, height h, and current I flowing through it, displaying closely wound turns.](image.png)1. **Calculate \( B \)**, the magnitude of the magnetic field produced by \( I \) inside the solenoid.2. **Calculate \( u_B \)**, the magnetic energy density inside the solenoid.3. Integrate the magnetic energy density in the volume to obtain \( U_B \), the magnetic energy stored in the solenoid.4. The energy stored in an inductor of self-inductance \( L \) can also be expressed as \( U_B = \frac{1}{2} L I^2 \). Use the result of part 3 to calculate the self-inductance of the solenoid.

Answered: Image /qna-images/answer/af8c0937-5a3f-448c-844e-f03db7c6d98f.jpg

Answered: energy stored in inductor

Science

Physics

energy stored in inductor

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Related questions

Q: The switch in a R-L circuit is closed allowing current to flow from a 12 volt battery. If the…

A: In R-L circuit, The potential difference of the battery is V = 12 V. The resistance of the resistor…

Q: 1. The current in a 7.50-H inductor is given by i=1.82-6.2t. Find the voltage inductor at 2.75s.…

A: Inductance, L = 7.50 HCurrent equation, i = 1.8t² - 6.2tAt t = 2.75 s

Q: When the number of loops of wire in a coil is doubled, assuming all the other factors stay constant,…

Q: A solenoid is 0.5 m long, has a diameter of 20 cm and is wound with 1200 turns of wire. Calculate…

A: Length(l)=0.5m Diameterd=20cm ⇒r=10 cm =0.1m n=1200

Q: Induttor 10.00 5.00 0.00 -5.00 H 0.00 0.50 1.00 Time (s) x10 Is inductor Voltage leading inductor…

A: The leading or lagging of voltage depends upon what colour represents voltage .

Q: 7. Consider a circuit with an inductor, a DC voltage source, a resistor, and an open switch.…

Q: # 11. If you double the number of turns and double the length of a solenoid by what factor will the…

A: The inductance of a solenoid is given by the expression

Q: If a solenoid is 10 cm long and has a radius of 1 cm, how many coils would be necessary to make an…

Q: If the value of inductance is 20 H and 4A of current flows through it, Find the value of energy…

A: Write the given values of this problem. L=20 HI=4 A

Q: ir own cir

A: Given as, A voltage source of V=86V A resistor of resistance R=1.8KΩ=1800Ω A inductor of inductance…

Q: 5. In an electric circuit containing inductors, the largest induced voltage usually occurs is opened…

Q: #71. At fixed length h of the coil, find the the self-inductance L when N and cross-sectional area A…

A: The self-inductance for a coil is given as: L=μ0N2Ah Where: μ0 is the Permeability of Free…

Q: (a) How much energy is stored in a 10.2 mH inductor carrying a 1.15 A current?

A: Given inductance is 10.2 mH Current is 1.15A

Q: R, = 1.3n 1.5 A R = 1.52 R3 = 1.82 20V

A: According to the Kirchoff's law, the direction of loop is from higher potential to lower potential.

Q: Explain how induction occurs.

Q: magnetic energy stored by a 4.56 mH inductor when the current through it is 10.3 A

A: Given Self inductance L = 4.56 mH = 4.56 × 10-3 H Current I = 10.3 A

Q: 8) Atwhat rate would the current in a I00-mH inductor have to change to induce an emf of 1000 V? A)…

Q: How fast can the 145 A current through a 0.240 H inductor be shut off if the induced emf cannot…

A: Given: Current is I=145 A Inductance of inductor is L=0.240 H Induced emf is emf=73 V Find: Time…

Q: What value of resistor R gives the circuit in (Figure 1) a time constant of 22 us?

A: To determine the value of R for T=22

Q: For the circuit shown, what is the rate of change of the current in the inductor when the current in…

A: Solution: It is given that, Current in the battery(I)=0.30 A

Q: Since inductors can be used as energy storage elements, how much inductance is needed to power up a…

Q: An inductor works as a _circuit for DC supply* Open O Non-Polar Short Polar

Q: 59. Starting with emf2 = -M- ΔΙ show that the units of Δι inductance are (V · s)/A = 2 · s.

A: Here, in the equation M is a mutual inductance, which has the same unit as inductance Emf unit is V…

Q: A solenoid with an inductance of 10.0 H has 1.0 x 10 A of current going through it. How much energy…

Q: 4. List the magnetic permeability and inductance values of some important materials: iron, steel,…

Q: 10. The number of turns in a solenoid is increased by a factor of three without changing the length.…

A: The given condition of the number of turns is given as N2=3N1 Here, N2 and N1 are the final number…

Q: voltage equal to the emf

Q: Find the energy stored in a 6.8-mH inductor when the current is 3.7 A.

A: Given, Inductance(L) = 6.8*10-3 Current(I) = 3.7 Ampere

Q: (L11) A 1.96 A current, constant in time, is applied to a 2.29E-3 H inductor. What is the voltage…

A: Current ( I ) = 1.96 A Inductance ( L ) = 2.29 10-3 H or L = 0.00229 H

Q: How much current would have to pass through a 10.0 mH inductor s would be enough to bring…

A: Hi please find solution to your problem Formula used E = 1/2 *L*I^2

Q: 10. An electric power station that operates at 15 kV and uses a 20:1 step-up ideal transformer is…

A: Given data; The output voltage of the transformer is V=20×15=300 kV The produced power is P=300 MW…

Q: Write any word problem with the graph below and a 50-mhenry inductor

A: Given, Inductor = 50 mH We need to :- Write any word problem with given graph and a 50-mhenry…

Q: The voltage across an inductor is proportional to the inductor and the derivative of the current…

A: As we know that, Voltage across Inductor is given by :…

Q: Is more energy stored in an inductor by doubling the inductance or by doubling thecurrent?

A: To determine: Whether the energy stored is more or not by doubling the inductance or the current.

Q: Explain the term mutual inductance.

A: Mutual inductance between the two coils is known as the property of the coil due to which it is…

Q: Describe the relationship between the charge and current oscillating between a capacitor and…

Q: An induced EMF of 16 V exists in a coil when the current in the coil changes at a rate of 42 A/s.…

Q: What is the difference between Self-inductance and Mutual inductance?

A: In electromagnetism and electronics, Inductance is a property of the electric which induces the…

Q: A-At time t = 0 the charge on the capacitor in the circuit of (figure 3) is 1 coulomb, while the…

A: For capacitorq=Qe-t/RCFor inductori=E/R(1-e-Rt/L)

Q: Find the energy stored in a 7.4-mH inductor when the current is 3.5 A. J

A: L=7.4mH=7.4×10-3HI=3.5A

Q: Why can a hum usually be heard when a transformer is operating?

A: A transformer is a device which is used to convert high to low and low to high ac voltages.

Q: 5. Determine the current as a function of time for the following circuit: (20 pt) E=10 volt and is…

Question

energy stored in inductor

In the figure below, you see a solenoid which has radius \( R \), height \( h \), \( N \) number of turns, and \( n \) number of turns per unit length. Consider its height to be much larger than its radius, so that we can assume the magnetic field to be uniform inside the solenoid and zero outside it, when a current \( I \) is flowing through the coils.

![Diagram of a solenoid with radius R, height h, and current I flowing through it, displaying closely wound turns.](image.png)

1. **Calculate \( B \)**, the magnitude of the magnetic field produced by \( I \) inside the solenoid.

2. **Calculate \( u_B \)**, the magnetic energy density inside the solenoid.

3. Integrate the magnetic energy density in the volume to obtain \( U_B \), the magnetic energy stored in the solenoid.

4. The energy stored in an inductor of self-inductance \( L \) can also be expressed as \( U_B = \frac{1}{2} L I^2 \). Use the result of part 3 to calculate the self-inductance of the solenoid.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step by step

Solved in 4 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

Why will a transformer not work if you are using dc?
11 - Four resistors, one uncharged capacitor and two inductors are arranged as shown in the figure. Then a potential difference eo is applied across the circuit as shown. Just after S is closed, what is the current through resistor R3 ? R2 R, a R3 LI L2 R 4. а) R1+R2+R3+RĄ E0 b) R1+R4 E0 c) R3 e) O R1+R2+R3 Boş bırak
Inductors Item 1
How inductance is used in traffic lights?
7) A circuit contains a 9 V battery, a 5 MQ resistor, a 10 H inductor, and a switch. When the switch is closed, what isthe current in the circuit after 1 usec?
Explain why charge or current oscillates between a capacitor and inductor, respectively, when wired in series
3. Calculate the self inductance on an inductor of 20 mH if the curren through it is increased uniformly from 0 to 4 A in 0.5 s?
1
Will a transformer operate if a battery is used for the input voltage across the primary? Explain.
21. Determine the inductance of a solenoid with 660 turns in a length of 34 cm. The circular cross section of the solenoid has a radius of 4.6 cm. Chap 23_#50
3) A resistor R is in series with a 8mH inductor. What value of R gives this circuit a time constant of 25µs?
what is inductance of coaxial cable what is inductance of coarialcable of length a' änd outer conductor raelius 68 inner conductor radius se