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 = br, 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: Ho, r, r2, b, R.) (a) r, < R B = (b) r2 > R B =

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 = br, 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: Ho, r, r2, b, R.) (a) r, < R B = (b) r2 > R B =

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter12: Sources Of Magnetic Fields

Section: Chapter Questions

Problem 25P: A long, straight, horizontal wire carries a left-to-right current of 20 A. If the wire is placed in...

See similar textbooks

Similar questions

A wire element has dI,IdI=JAdl=Jdv , where A and dv are the cross-sectional area and volume of the element, respectively. Use this, the Biot-Savart law, and J=nev to show that the magnetic field of a moving point charge q is given by: B=04qvrr2
A strip of copper is placed in a uniform magnetic field of magnitude 2.5 T. The Hall electric field is measured to be 1.5103V/m (a) What is the drift speed of the conduction electrons? (b) Assuming that n =8.01028 elections per cubic meter and that the cross-sectional area of the strip is 5.0106m2 , calculate the current in the ship, (c) What is the Hall coefficient 1/nq?
A long, straight, horizontal wire carries a left-to-right current of 20 A. If the wire is placed in a uniform magnetic field of magnitude 4.0105 T that is directed vertically downward, what is tire resultant magnitude of the magnetic field 20 cm above the wire? 20 cm below the wire?
Repeat the previous problem, but with the loop lying flat on the ground with its current circulating counterclockwise (when viewed from above) in a location where Earth’s field is north, but at an angle 45.0° below the horizontal and with a strength of 6.0105T.
Consider the axial magnetic field Bv=0IR2/2(y2+R2)3/2 of the circular current loop shown below. (a) Evaluate aaBydy Also show that limaaaBydy=0I (b) Can you deduce this limit without evaluating the integral? (Hint: See the accompanying figure.)
A long, straight wire of radius R caries a current I that is distributed uniformly over the cross-section of the wire. At what distance from the axis of the wire is the magnitude of the magnetic field a maximum?
A long, straight, cylindrical conductor contains a cylindrical cavity whose axis is displaced by n from the axis of the conductor, as shown in the accompanying figure. The current density in the conductor is given by J=J0k, where J0 is a constant and k is along the axis of the conductor. Calculate the magnetic field at an arbitrary point P in the cavity by superimposing the field of a solid cylindrical conductor with radius R1and current density Jonto the field of a solid cylindrical conductor with radius R2and current density J . Then use the fact that the appropriate azimuthal unit vectors can be expressed as 1=kr1and 2=kr2 to show that everywhere inside the cavity the magnetic field is given by the constant B=120J0ka , where a=r1r2 and r1=r1r1 is the position of P relative to the center of the conductor and r2=r2r2 is the position of P relative to the center of the cavity.
A wire ismade into a circular shape of radius R and pivoted along a central support.The two ends of the sire are touching a banish that is connected to a &power source. The stricture is between the poles of a magnet such that we can assume there is a uniform magnetic field on the wire. In terms of a coordinate system with origin at the center ofthe ring, magneticfieldisBx=B0,By=Bz= 0. and the ring rotates about the z-axis. Find the torque on the ring siren it is not in the xz-plane.
The current loop shown in the accompanying figure lies in the plane of the page, as does the magnetic field. Determine the net force and the net torque on the loop if I=10and B=1.5T .
A circular loop of wire of radius 10 cm is mounted on a vertical shaft and rotated at a frequency of 5 cycles per second in a region of uniform magnetic field of 2 Gauss perpendicular to the axis of rotation, (a) Find an expression for the time-dependent flux through the ring, (b) Determine the time-dependent current through the ring if it has a resistance of 10
Determine the magnetic field on the central axis at the opening of a semi-infinite solenoid. (That is, take the opening to be at x = 0 and the other end to be at x= .)
The figure below shows a cylindrical conductive shell carrying current I to the right. The current density (non-uniform) in the conductor is given by J=c(r−R1) for the region R1<r<R2, where c is a constant. What is the magnitude of the magnetic field at a radial distance rA inside the conductor.