Concept explainers
The magnitude J(r) of the current density in a certain cylindrical wire is given as a function of radial distance from the center of the wire’s cross section as J(r) = Br, where r is in meters, J is in amperes per square meter, and B = 2.00 × 105 A/m3. This function applies out to the wire’s radius of 2.00 mm. How much current is contained within the width of a thin ring concentric with the wire if the ring has a radial width of 10.0 µm and is at a radial distance of 1.20 mm?
Want to see the full answer?
Check out a sample textbook solutionChapter 26 Solutions
Fundamentals Of Physics - Volume 1 Only
Additional Science Textbook Solutions
Essential University Physics (3rd Edition)
Glencoe Physics: Principles and Problems, Student Edition
University Physics Volume 3
Conceptual Physics (12th Edition)
Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)
Lecture- Tutorials for Introductory Astronomy
- The beam, consisting of electrons with constant kinetic energy and uniform density, carries a current of 1 mA. The cross-section-area of the beam is 23 mm², the electron density is 3x10^12 cm-3. If the electric current is directed to the right, what is the magnitude (m/s) and direction of the velocity of the electrons?arrow_forwardIf the current carried by a conductor is doubled, what happens to (a) the charge carrier density, (b) the current density, (c) the electron drift velocity, and (d) the average time interval between collisions?arrow_forwardWhat is the current in a wire of radius R = 4.48 mm if the magnitude of the current density is given by (a) Ja = J0r/R and (b) Jb = J0(1 - r/R) in which r is the radial distance and J0 = 7.93 × 104 A/m2? (c) Which function maximizes the currentdensity near the wire’s surface?arrow_forward
- The normal vector from region 2 to region 1 is ân21=(6âx+2ây-3âz)/7. If H1=10âx+ây+12âz A/m and H2=H2x âx-5ây+4âz A/m, find the surface current density at the interface. (μ1=2μ0 ve μ2=μ0)arrow_forwardA high-voltage transmission line with a diameter of 2.00 cm and a length of 200 km carries a steady currentof 1 000 A. If the conductor is copper wire with a freecharge density of 8.46 ×1028 electrons/m3, over whattime interval does one electron travel the full length of the line?arrow_forwardA beam of doubly charged negative ions with a number density of 2.7 × 1018 cm−3 is traveling north with a speed of 1.0 × 105 m/s. What are the (a) magnitude and (b) direction of the current density?arrow_forward
- A long, straight, solid cylinder, oriented with its axis in the z−direction, carries a current whose current density is J⃗. The current density, although symmetrical about the cylinder axis, is not constant but varies according to the relationship J⃗=2*I0/πa^2 *[1−(r/a)^2]k for r≤a=0 for r≥a where a is the radius of the cylinder, r is the radial distance from the cylinder axis, and I0 is a constant having units of amperes. Part A Using Ampere's law, derive an expression for the magnitude of the magnetic field B⃗ in the region r≥a. Part B Obtain an expression for the current I contained in a circular cross section of radius r≤a and centered at the cylinder axis. Part C Using Ampere's law, derive an expression for the magnitude of the magnetic field B⃗ in the region r≤a.arrow_forwardThe electric field of the material between two coaxial cables of radius 0.525 cm and 0.675 cm is given as E = 2.85 V.m/r3 . If the conductivity of the material is 5 x 1010 S/m, what is the current density in the material?arrow_forwardQ-1 An iron wire with cross section 2.5x10^-6 m^2 carries current 126 A. Find the drift velocity Vd, in units of millimeters per second, by assuming the existence of two carriers per iron atom.arrow_forward
- A long coaxial cable, crossection of which is shown in the figure, is made up of a cylindrical inner wire of radius a and a cylindrical shell shaped coaxial outer wire of inner radius b and outer radius c. The current density with magnitude J = Kr2/a is spread over the cross section of the inner wire where the current has out-of-page direction. Outer wire carries uniformly distributed current i = πKa 3 having into-the-page direction. a) Find the total current of the inner wire iin in terms of ?.Find expressions for the magnitude of magnetic field, b) inside the inner wire (r < a) c) between the wires (a< r< b) d) inside the outer wire (b< r < c) e) outside the outer wire (r> c) in terms of i, π, μ and r. For each case indicate the direction of the magnetic field as well.arrow_forwardConsider two wires made of different materials. Wire A has a conductivity of 1.3 × 107 Ω-1m-1, and wire B has a conductivity of 5.1 × 107 Ω-1m-1. Wire A has a circular cross-section with radius 3.78 mm. If there is an electric field of 0.085 V/m inside it, how much current, in amperes, is flowing through it? Wire B has a square 3.78 mm × 3.78 mm cross-section. If wire B has the same electric field as Wire A did in part (a), what current, in amperes, would be passing through it?arrow_forwardThe vector current density of a 3m long and 3mm diameter conductor is given as 155630 A/m^2. Determine the curent on the conductor, its free electron density, the drift velocity of the charges and the number of electrons passing through the conductor for 3 seconds.arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning