Chapter 29 Magnetic Fields Due to Currents In this chapter we will explore the relationship between an electric current and the magnetic field it generates in the space around it. We will follow a two-prong approach, depending on the symmetry of the problem. For problems with low symmetry we will use the law of Biot-Savart in combination with the principle of superposition. For problems with high symmetry we will introduce Ampere’s law. Both approaches will be used to explore the magnetic field generated by currents in a variety of geometries (straight wire, wire loop, solenoid coil, toroid coil) We will also determine the force between two parallel current carrying conductors. We will then use this force to define the SI unit for electric current (the Ampere) (29 – 1)

of their speeds, vproton/valpha, is: A proton (charge e), traveling perpendicular to a magnetic field, experiences the same force as an alpha particle (charge 2e) which is also traveling perpendicular to the same field. The ratio of their speeds, vproton/valpha, is: A. 0.5 B. 1 C. 2 D. 4 E. 8 c

A proton (charge e), traveling perpendicular to a magnetic field in a circular orbit, experiences the same force as an alpha particle (charge 2e, mass 4p) which is also traveling perpendicular to the same field. The ratio of their orbital radii rproton/ralpha, is: A. 0.5 B. 1 C. 2 D. 4 E. 8 A proton (charge e), traveling perpendicular to a magnetic field in a circular orbit, experiences the same force as an alpha particle (charge 2e, mass 4p) which is also traveling perpendicular to the same field. The ratio of their orbital frequency fproton /f alpha is: B

A (29 – 2)

(29 – 3)

(29 – 4)

. (29 – 5)

(29 – 6)

(29 – 7)

(29 – 8)

(29 – 9)

R r B O (29 – 10)

(29 – 11)

(29 – 12)

(29 – 13)

(29 – 14)

An electron and a proton each travel with equal speeds around circular orbits in the same uniform magnetic field. The field is into the page. Because the electron is less massive than the proton and because the electron is negatively charged and the proton is positively charged: A. the electron travels clockwise around the smaller circle and the proton travels counter- clockwise around the larger circle B. the electron travels counterclockwise around the smaller circle and the proton travels clockwise around the larger circle C. the electron travels clockwise around the larger circle and the proton travels counterclockwise around the smaller circle D. the electron travels counterclockwise around the larger circle and the proton travels clock- wise around the smaller circle E. the electron travels counterclockwise around the smaller circle and the proton travels counterclockwise around the larger circle A

A. opposite the direction of the current The diagram shows a straight wire carrying current i in a uniform magnetic field. The magnetic force on the wire is indicated by an arrow but the magnetic field is not shown. Of the following possibilities, the direction of the magnetic field is: i F A. opposite the direction of the current B. opposite the direction of ~F C. in the direction of ~F D. into the page E. out of the page E

The magnitude of the magnetic field at point P, at the center of the semicircle shown, is given by: i A. 2μ0i/R B. μ0i/R C. μ0i/4πR D. μ0i/2R E. μ0i/4R P