PHY 112 (SECTION 001 ) Lecture 12,13 Chapter 28 of R Haliday Book

Outline Magnetic field ( ) Hall Effect (28-5), Magnetic Force on a Current Carrying Wire (28-8). Torque on a Current Loop (28-9). Biot-Savart Law (29-2), Force Between Parallel Currents (29-3). Ampere's Law (29-4), Solenoids and Toroids (29-5) Fall 2011 (PHY 112 Section 1) 2

What Produces a Magnetic Field? One way is to use moving electrically charged particles, such as a current in a wire, to make an electromagnet. The current produces a magnetic field that can be used. (computer hard drive). The other way to produce a magnetic field is by means of elementary particles (such as electrons) because these particles have an intrinsic magnetic field around them. That is, the magnetic field is a basic characteristic of each particle just as mass and electric charge (or lack of charge) are basic characteristics. Fall 2011 (PHY 112 Section 1) 3

4

5

6

Direction of F The right-hand rule Fall 2011 (PHY 112 Section 1) 7

8

Lines of Mag Field Fall 2011 (PHY 112 Section 1) 9

10

Fall 2011 (PHY 112 Section 1) 11

HALL EFFECT A beam of electrons in a vacuum can be deflected by a magnetic field. Can the drifting conduction electrons in a copper wire also be deflected by a magnetic field? In 1879, Edwin H. Hall, then a 24-year-old graduate student at the Johns Hopkins University, showed that they can. This Hall effect allows us to find out whether the charge carriers in a conductor are positively or negatively charged. Beyond that, we can measure the number of such carriers per unit volume of the conductor. Fall 2011 (PHY 112 Section 1) 12

Figure 28-8a shows a copper strip of width d, carrying a current i whose conventional direction is from the top of the figure to the bottom. The charge carriers are electrons and, as we know they drift (with drift speed v d ) in the opposite directior, from bottom to top. Fall 2011 (PHY 112 Section 1) 13

Fall 2011 (PHY 112 Section 1) 14

Fall 2011 (PHY 112 Section 1) 15

A flexible wire passes between the pole faces of a magnet. (a)Without current in the wire, the wire is straight. (b)With upward current, the wire is deflected rightward. (c)With downward current, the deflection is leftward. The connections for getting the current into the wire at one end and out of it at the other end are not shown. Magnetic Force on a current carrying conductor Fall 2011 (PHY 112 Section 1) 16

Fall 2011 (PHY 112 Section 1) 17

Fall 2011 (PHY 112 Section 1) 18

A curved wire carries a current A curved wire carrying a current I in a uniform magnetic field. The total magnetic force acting on the wire is equivalent to the force on a straight wire of length L’ running between the ends of the curved wire. Fall 2011 (PHY 112 Section 1) 19

A current-carrying loop of arbitrary shape A current-carrying loop of arbitrary shape in a uniform magnetic field. The net magnetic force on the loop is zero. Fall 2011 (PHY 112 Section 1) 20

Calculating the Magnetic Field Due to a Current A wire of arbitrary shape carrying a current i. We want to find the magnetic field B at a nearby point p. Biot–Savart law:

The right-hand rule for determining the direction of the magnetic field surrounding a long, straight wire carrying a current. Note that the magnetic field lines form circles around the wire.

Magnetic Field of a Solenoid It concerns the magnetic field produced by the current in a long, tightly wound helical coil of wire. Such a coil is called a solenoid (Fig ). We assume that the length of the solenoid is much greater than the diameter.

Magnetic Field of a Toroid Figure a shows a toroid, which we may describe as a (hollow) solenoid that has been curved until its two ends meet, forming a sort of hollow bracelet.

Magnetic Field Due to a straight Wire Segment Magnetic Field Due to a straight

Magnetic Field Due to a curved Wire Segment The magnetic field at O due to the current in the curved segment AC is into the page. The contribution to the field at O due to the current in the two straight segments is zero. The magnetic field at O due to the current in the straight segments AA’ and CC’ is zero because ds is parallel to along these paths; Each length element ds along path AC is at the same distance R from O, and the current in each contributes a field element dB directed into the page at O. Furthermore, at every point on AC, ds is perpendicular to hence,

The direction of B is into the page at O because ds×r is into the page for every length element.

Magnetic Field on the axis of a Circular Current Loop

Magnetic field lines surrounding a current loop.

THE MAGNETIC FORCE BETWEEN TWO PARALLEL CONDUCTORS

Magnetic Field Outside a Long Straight Wire with Current