A solenoid of a radius R wound with n turns per unit lengthcarries a current given by I = I0e −βt, where t is the time and β > 0.What are the magnitude and direction of the induced electric field justoutside the solenoid?

A solenoid of a radius R wound with n turns per unit lengthcarries a current given by I = I0e −βt, where t is the time and β > 0.What are the magnitude and direction of the induced electric field justoutside the solenoid?

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter13: Electromagnetic Induction

Section: Chapter Questions

Problem 89CP: A long solenoid of radius a with n turns per unit length is carrying a tune-dependent current...

See similar textbooks

Related questions

Q: A long thin solenoid has 779 turns per meter and radius 2.00cm. The current in the solenoid is…

Q: An infinite straight wire carries current I1 = 4.3 A in the positive y-direction as shown. At time t…

A: As per guidelines we are suppose to do only three subpart from multipart questions, and one from…

Q: The rectangular loop shown in the figure is pushed into the magnetic field which points inward. X X…

Q: The figure shows two closed paths wrapped around two conducting loops carrying currents i1 = 5.0 A…

A: Given: The two conducting loops carrying currents i1 = 5.0 A and i2 = 3.0 A. To determine: the…

Q: A long solenoid has a radius of 4 cm and has 800 turns/m. If the current in the solenoid is…

Q: If 50.0 cm of copper wire (diameter = 1.00 mm) isformed into a circular loop and placed…

Q: How many A/m is the magnetic field strength (H) at the point 1.8 m away from the infinitely long…

A: Given Data: The distance of the point is: r=1.8 m The current is long wire is: I=2 A The magnetic…

Q: A small airplane with a wing span of 11 m flies horizontally and due north at a speed of 67 m/s in a…

Q: An ideal solenoid of radius a has n turns per unit length and current I. The magnetic fluxog through…

Q: A long solenoid of radius a with n turns per unit length is carrying a time-dependent current I(t) =…

Q: The figure shows a circular loop of radius a=2.1 cm concentric with a circular arc of radius b-3.6…

Q: 12. A 15 µC charged particle is shot through the interior of a solenoid with a speed of 1050 m/s and…

A: Given, Charge particle q = 15 μC = 15 x 10-6 C Speed v = 1050 M/s Angle θ=11.5∘ Length of solenoid l…

Q: Two very long solenoids have the same length, but solenoid A has 18 times the number of turns, 1/4…

A: Use formula of magnetic field at inside of solenoid and put the given values to calculate ratio .…

Q: A loop of radius a = 9.5 cm lays in the x-y plane, in a region of uniform, time-dependent magnetic…

A: Radius of circular loop (R) = 9.5 cm = 0.095 m Magnetic field ( B[t]) = 1.6 t Resistance (R) = 4.1…

Q: A Boeing 747 aircraft with a wingspan of 65 m is cruising at 260 m/s over northern Canada, where the…

Q: What should be the length of an ideal solenoid consisting of 1250 turns for the magnetic field in…

A: The coils that are able to produce magnetic field which is uniform like from a bar magnet , due to…

Q: Consider a conducting rod of length 29 cm moving along a pair of rails, and a magnetic field…

Q: An infinite straight wire carries current l₁ = 3.7 A in the positive y- direction as shown. At time…

Q: A long thin solenoid has 808 turns per meter and radius 3.00cm. The current in the solenoid is…

Q: Two solenoids are nested coaxially such that their magnetic fields point in opposite directions.…

A: Given: The radius of the outer solenoid is ro=20 mm=20×10-3m The length of the outer solenoid is…

Q: In the figure, an electron with an initial kinetic energy of 4.10 keV enters region 1 at time t = 0.…

A: When a charged particle enters magnetic field which is perpendicular to it then its speed remains…

Q: A square loop of each side as 'a' and a circular loop with the diameter of length 'a' lie in the…

Q: A rectangular loop of wire with total resistance R = 1500 N is fixed in place near an infinitely…

A: Given:- A rectangular loop of wire with total resistance R 1500 12 is fixed in place near an…

Q: What current is required in the windings of a long solenoid that has 1000 turns uniformly…

A: Number of turns (N) = 1000 Magnetic field (B) = 1×10-4 T Length (L) = 0.40 m Number of turns per…

Q: A solenoid of length L=26 cm and cross-sectional area A=49 cm2 with N=81 turns of wire is carrying a…

Q: As shown, a single loop (resistance R, width W, and length L) moves to the right at a constant speed…

Q: A coaxial cable is constructed from a central cylindrical conductor of radius A = 1.10 cm carrying…

Q: By how much is the approximation B = μ0 nI in error at the center of a solenoid that is 15.0 cm…

A: Given data The length of the solenoid is L=15 cm The diameter is, d=4.0 cm The approximate magnetic…

Q: In Fig. 2, an electron with an initial kinetic energy of 5.0 keV enters region 1 at time t= 0. That…

A: Given data: Points to keep in mind, When the electron enters the regions (1) and (2), it will…

Q: (1) ta

A: Given: r0=0.1 mv=0.015 m/sR=12 ΩB0=0.75 Tt=5 s

Q: A square loop of dimensions 5.0 cm x 5.0 cm is initially in a 0.80-Tesla magnetic field, with its…

A: The area of the loop A= 5.0 cm x 5.0 cm = 25 cm2 =25×10-4 m2 The magnetic field intensity B = 0.8 T…

Q: A horizontal metal bar oriented east-west, is dropped straight down at a place where Earth's…

A: here,F=qV×Baccording to right hand rule, if the right hand is placed as if to grasp the wire, with…

Q: A conducting rod with length L = 18.6 cm is being pulled along a long rotated U-shape conductor,…

A: Write the expression for the induced emf and substitute the required values.

Q: A long solenoid has a radius of 4 cm and has 800 turns/m. If the current in the solenoid is…

A: option (e) is correct.

Q: How much energy is stored in a cylindrical solenoid of length 0.734 m and radius 0.0509 m which has…

Q: A closely wound solenoid of 2000 turns has an axial length of 64 cm and a radius of 2.50 cm. When…

A: The formula for magnetic flux density or magnetic field is given by B = μ0nI = μ0NI /H where μ0 =…

Q: Q. # 1: A conductor of length "r" and mass “m" can slide along a pair of vertical metal guides…

A: Given Data: The length of the conductor is l. The mass of the conductor is m. The resistance of…

Q: An 800 turns solenoid of length L= 0.4 m, radius R=10 cm, producing a uniform magnetic field B =…

A: We have to use some basic formula here.

Q: What current is required in the windings of a solenoid that has 900 turns evenly distributed over a…

A: Given data: Number of turns (N) = 900 Length (L) = 0.5 m Magnetic field (B) = 7 × 10-3 T Required:…

Q: .. Using Ampere's law derive an expression for the magnetic field due to a long, hollow cylindrical…

Q: You are given a straight piece of conductor that is 5.0 cm long and moves in a region of uniform…

Q: Consider a square loop with side length 1m moving at a rate 0.1 m/s in the +x-direction into a…

A: side length of square loop (L) = 1 m velocity (v) = 0.1 m/s magnetic field (B) = 1 T t = 5 sec

Q: A tightly-wound toroidal solenoid has a central radius (the radius midway between the inner and…

A: According to the formula used for the magnetic field inside the Toroidal solenoid which is given b…

Q: For a current-carrying loop attached to a fixed axis in a uniform magnetic field, what is the phase…

A: Required : What is the angular difference between when the flux is maximum and when the torque is…

Concept explainers

Ferromagnetism

Ferromagnetism is a mechanism by which some materials show magnetic properties. Iron and magnetite, an oxide of iron, are two naturally occurring materials that show the property of ferromagnetism. The word ferromagnetism is derived from the Latin name of iron, "Ferrum" as it was the first observed material to show such property. The property of ferromagnetism is shown by only a few substances such as iron, nickel, cobalt, and their alloys. Some transition metals and alloys of rare-earth metals also show ferromagnetism.

Question

A solenoid of a radius R wound with n turns per unit length
carries a current given by I = I0e −βt, where t is the time and β > 0.
What are the magnitude and direction of the induced electric field just
outside 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

Assume the region to the right of a certain plane contains a uniform magnetic field of magnitude 1.00 mT and the field is zero in the region to the left of the plane as shown in Figure P22.71. An electron, originally traveling perpendicular to the boundary plane, passes into the region of the field. (a) Determine the time interval required for the electron to leave the field-filled region, noting that the electrons path is a semicircle. (b) Assuming the maximum depth of penetration into the field is 2.00 cm, find the kinetic energy of the electron.
Two long coaxial copper tubes, each of length L, are connected to a battery of voltage V. The inner tube has inner radius o and outer radius b, and the outer tube has inner radius c and outer radius d. The tubes are then disconnected from the battery and rotated in the same direction at angular speed of radians per second about their common axis. Find the magnetic field (a) at a point inside the space enclosed by the inner tube r d. (Hint: Hunk of copper tubes as a capacitor and find the charge density based on the voltage applied, Q=VC, C=20LIn(c/b) .)
The conducting rod shown in the accompanying figure moves along parallel metal rails that are 25-cm apart. The system is in a uniform magnetic field of strength 0.75 T, which is directed into the page. The resistances of the rod and the rails are negligible, but the section PQ has a resistance of 0.25 . (a) What is the emf (including its sense) induced in the rod when it is moving to tire right with a speed of 5.0 m/s? (b) What force is required to keep the rod moving at this speed? (c) What is the rate at which work is done by this force? (d) What is the power dissipated in the resistor?
A toroid has a major radius R and a minor radius r and is tightly wound with N turns of wire on a hollow cardboard torus. Figure P31.6 shows half of this toroid, allowing us to see its cross section. If R r, the magnetic field in the region enclosed by the wire is essentially the same as the magnetic field of a solenoid that has been bent into a large circle of radius R. Modeling the field as the uniform field of a long solenoid, show that the inductance of such a toroid is approximately L=120N2r2R Figure P31.6
A conducting single-turn circular loop with a total resistance of 5.00 is placed in a time-varying magnetic field that produces a magnetic flux through the loop given by B = a + bt2 ct3, where a = 4.00 Wb, b = 11.0 Wb/s2, and c = 6.00 Wb/s3. B is in webers, and t is in seconds. What is the maximum current induced in the loop during the time interval t = 0 to t = 3.50 s?
Two frictionless conducting rails separated by l = 55.0 cm are connected through a 2.00- resistor, and the circuit is completed by a bar that is free to slide on the rails (Fig. P32.71). A uniform magnetic field of 5.00 T directed out of the page permeates the region, a. What is the magnitude of the force Fp that must be applied so that the bar moves with a constant speed of 1.25 m/s to the right? b. What is the rate at which energy is dissipated through the 2.00- resistor in the circuit?
A circular loop of radius R carries a current I. At what distance along the axis of the loop is the magnetic field one- half its value at the center of the loop?
A solenoid has a ferromagnetic core, n = 1000 turns per meter, and I = 5.0 A. If B inside the solenoid is 2.0 T, what is for the core material?
When the current through a circular loop is 6.0 A, the magnetic field at its center is 2.0104 T. What is the radius of the loop?
A solenoid is 40 cm long, has a diameter of 3.0 cm, and is wound with 500 turns. If the current through the windings is 4.0 A, what is the magnetic field at a point on the axis of the solenoid that is (a) at the center of the solenoid, (b) 10.0 cm from one end of the solenoid, and (c) 5.0 cm from one end of the solenoid? (d) Compare these answers with the infinite-solenoid case.
Solenoid A has length L and N turns, solenoid B has length 2L and N turns, and solenoid C has length L/2 and 2N turns. If each solenoid carries the same current, rank the magnitudes of the magnetic fields in the centers of the solenoids from largest to smallest.
How is the percentage change in the strength of the magnetic field across the face of the toroid related to the percentage change in the radial distance from the axis of the toroid?