The diagram below shows an infinitely long straight wire with a current I that is directed in the +x direction. The ultimate goal of this problem is to use the Biot Savart Law to derive the magnetic field by the wire at point P which is a distance d from the wire. P +y I ds, 1 dB 1₂ - [H-1² 4T +z ds 2 The Biot Savart Law gives an expression of the magnetic field by a infinitesimal segment of the wire. Hods x f p2 +x Notice that the direction of the field corresponding to a current segment (dB) is given by the direction of the cross product ds x î.

The diagram below shows an infinitely long straight wire with a current I that is directed in the +x direction. The ultimate goal of this problem is to use the Biot Savart Law to derive the magnetic field by the wire at point P which is a distance d from the wire. P +y I ds, 1 dB 1₂ - [H-1² 4T +z ds 2 The Biot Savart Law gives an expression of the magnetic field by a infinitesimal segment of the wire. Hods x f p2 +x Notice that the direction of the field corresponding to a current segment (dB) is given by the direction of the cross product ds x î.

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

Similar questions

Each of the two "infinite" parallel wires (perpendicular to the plane of the page) carries a current of I=1.65 A. The direction each current is shown with a dot or a cross; a=0.168 m.Find the magnitude of the magnetic field at a point A: BA= T.This field is directed to? Find the magnitude of the magnetic field at a point B: BB= T.This field is directed to?
A coaxial cable consists of a long thin wire surrounded by a cylindrical conductor of radius 5mm. A current of 20A flows to the right in the wire and an equal current flows to the left in the outer conductor. Using Ampere’s law, find the magnetic field at a point 2.5 mm from the central wire, and a point 2.5 cm from the central wire. Sketch the magnetic field lines.
A long, cylindrical conductor of radius R carries a current I as shown in the figure below. The current density J, however, is not uniform over the cross-section of the conductor but is a function of the radius according to J = 6br2, where b is a constant.Find an expression for the magnetic field magnitude B at the following distances, measured from the axis. (Use the following variables as necessary: ?0, r1, r2, b, R.) (a) r1 < RB = (b) r2 > R B =
A wire carrying 1.5 A passes through a 48-mT magnetic field. The wire is perpendicular to the field and makes a quarter-circle turn of radius 21 cm as it passes through the field region, as shown in (Figure 1). Figure 1.5 A- X X X X X 21 cm Bin X X X X X X Part A Find the magnitude of the magnetic force on this section of wire. Express your answer in newtons. F= Submit Part B Η ΑΣΦ Submit Request Answer ΕΠ ΑΣΦ Find the direction angle of the magnetic force on this section of wire. The angle is measured from the rightward direction toward the upward direction. Express your answer in degrees. " Request Answer Ò A 1 ? < Return to Assignment Provide Feedback N P ?
In the figure, point P, is at perpendicular distance R = 28.7 cm from one end of straight wire of length L = 14.6 cm carrying current i = 0.756 A. (Note that the wire is not long.) What is the magnitude of the magnetic field at P2? P R R L. Number i Units
In the figure, point P2 is at perpendicular distance R = 29.5 cm from one end of straight wire of length L = 13.4 cm carrying current i= 0.783 A. (Note that the wire is not long.) What is the magnitude of the magnetic field at P2? Po R I. Number i Units
A single ionized atom, that is deficient one electron, is traveling at in a straight line when it enters a uniform magnetic field of strength 0.750 T. The ion is traveling in the plane of the page, while the magnetic field points into the page. (See the diagram below.) If the mass of the ionized atom is 6.68 x 10-27 kg, what is the frequency in Hz of the resultant circular motion? The charge of a single electron is 1.602 x 10-19 C. a. 7.47 MHz b. 6.33 MHz c. 4.13 MHz d. 3.50 MHz e. .2.86 MHz
A square wire loop is on the x and y plane with the center is located on the origin (zero), and the sides are 20cm long. The wire has a 5.0A current traveling clockwise. What is the magnetic field vector at the origin? What is the magnetic field vector at x=5cm, y=0cm? What is the magnetic field vector at x=15cm, y=0cm?
Consider a short wire of length L, carrying a current I to the left. Define coordinates so that the wire is along the à axis, the current flows in the - direction, the y axis is vertical in the plane of the page and the 2 axis points out of the page. Which of the following expressions is an ap- proximate expression for the magnetic field at a point P on the y axis very close to the wire, i.e. a distance y < L below the mid- point of the wire? 1. B= 2(y2 + L2) O 2. B 0 3. B Hol 2ny Hol 4Vy2 + L² 4. B = Hol 4Ty 5. B = %3D O 6. B=-00 O, B = 47 (y2 + L2) 8. B = 27 Vy? + L2 40IL 2ny? 9. B = 10. B – _ 40! 2ny
An infinitely long, straight, cylindrical wire of radius R has a uniform current density J = Jî in cylindrical coordinates. What is the magnitude of the magnetic field at some point inside the wire at a distance r; < R from the wire's central Cross-sectional view axis? Express your answer in terms of R, r;, µo, and J. J B = Side view Assuming J is positive, what is the direction of the magnetic field at some point inside the wire? O positive z-direction negative z-direction positive r-direction negative r-direction positive p-direction negative p-direction
In the figure, point P2 is at perpendicular distance R = 26.0 cm from one end of straight wire of length L = 13.0 cm carrying current i = 0.849 A. (Note that the wire is not long.) What is the magnitude of the magnetic field at P2? P P R R L. Number i 4.245 Units
A circular closed, conducting loop of radius r is in the presence of a uniform magnetic field that points into the page, shown in the figure below. The strength of the magnetic field changes as a function of time, which is described by the following expression: B(t) = B1t? + Bo. You may assume that B1 and Bo are both positive numbers. The direction of the magnetic field stays constant. The total resistance of the conducting loop is R. Use this information to solve parts (a) - (d). Write your answers in terms of known quantities such as: r, R, B1, Bo, and t. B(t) = B,t? + Bo %3D R r (a) Write an expression for the magnetic flux through the loop, assuming that the area vector of the loop points out of the page. Is the flux increasing or decreasing over time? (b) Determine the magnitude of the induced electromotive force driven through the loop. (c) Determine the magnitude of the induced current driven through the loop. (d) In which direction does the induced current flow (clockwise or…