Chapter 13Magnetic Fields: VI a Forces on a Wire Carrying a Current in a magnetic Field Magnetic Pressure Magnetic Energy denisity a Magnetic Forces btwn Two electric Currents Magnetic Forces within an isolated Circuit
Chapter 13Magnetic Fields:VI ◼ Forces on a Wire Carrying a Current in a Magnetic Field ◼ Magnetic Pressure ◼ Magnetic Energy Denisity ◼ Magnetic Forces btwn Two Electric Currents ◼ Magnetic Forces Within an Isolated Circuit
In this chapter. we study magnetic energy and macroscopic forces In practice, magnetic forces are much larger than electric forces, and they have many more applications
In this Chapter, we study magnetic energy and macroscopic forces. In practice, magnetic forces are much larger than electric forces, and they have many more applications
13. 1 Force on a Wire Carrying a Current in a Mag netic Field We know the lorentz force: F=Qvx B Now look at a piece dl of wire carrying current l, a is its cross-section area, n is its density of electron Figure 13-I Wire of cross-section a carrying a current I. The charges - move at a velocity v. The magnetic field B is due to currents flowing elsewhere
Since the conduction electrons are moving the force on the wire is dF=madl(-ev×B) where nadl is the number of electrons in this piece of wire The current in the wire is I=-naev, So dF= Id x e=ldl×B where dl is in the direction of the current If it's straight length l in a uniform of b the en F=n1×B
th) Figure 13-2 Magnetic field near a current-carrying wire situated in a uniform magnetic field. (a) Lines of B for a current perpendicular to the paper. (b) Lines of B for a uniform field parallel to the paper. (c) Superposition of fields in(a) and (b) and the resulting magnetic force F. The wire carries a current of 10 amperes, the uniform field has a B of 2 x 10"tesla, and the point where the lines of B are broken is at 10 millimeters from the center of the wire
In the above example the force on the current l is just given by F=1B, and its direction is to the left The lines of B are plotted in Fig. 13-2 These lines are under tension and repel each other laterally, giving rise to magnetic forces
13.2 Magnetic Pressure A current sheet carries a current density a(am pere/meter). It generates B B y fB. dI=pol, taking a closed path around the current, we have B+B=10, so the magnetic field generated on both sides of the sheet is B its direction: one side is upward, another side is downward.(both⊥toa)
13.2M agnetic Pressure Now we put this sheet into a given uniform magnetic field=uo1 2 Thus on one side of the sheet the magnetic fields cancel, 10I/2-10I/2=0 and on the other side they add up 140I/2+p40 I/2=p0 /2
13.2 Magnetic Pressure Now we put this sheet into a given uniform magnetic field B=uoa 2 Thus on one side of the sheet the magnetic fields cancel 10O 140/2= and on the other side they add up 0a/2+10/2=10C=2B The force on the sheet per unit area(pressure)is =axB=a(10a/2)=a210/2=(2B)2/210
Conclusion: for a sheet carrying a current with a total magnetic field b on one side and zero mag- netic field on the other side the sheet is subject to a pressure Its direction is the same as if the b is replaced by a compressed gas The magnetic pressure here can be ascribed to the lateral repulsion of the magnetic lines
