Physics21 Magnetic Field Lines

Magnetic Field Sources

Magnetic Fields • A force field that denotes the area in which the noncontact force of permanent magnets or current carrying conductors can exert their influence • Fields are concentrated at the poles • Same properties with Electric field lines except that there is no magnetic monopole

Magnetic field lines

Magnetic Force

• Like poles repel, opposite attract • An object that contains iron but is not itself magnetized is attracted by either pole of a permanent magnet.

Magnetic Force

Magnetic interactions can be described as: • •

•

A moving charge or a current creates a magnetic field in the surrounding space (in addition to its electric field) The magnetic field exerts a force Fm on any other moving charge or current that is present in the field. The magnetic force Fm acting on a positive charge q moving with velocity v is perpendicular to both Fm and the magnetic field B.

Units of Magnetic Fields • SI units: tesla, T 1 tesla = 1 T = 1 N/A·m • Or: gauss, G 1 G = 10-4 T

Magnetic Force on Moving Charge • Moving charged particles are deflected in magnetic r r r fields F  q v  B • Right-Hand Rule

Grip and Hand Rules

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Magnetic Force on Moving Charge The magnetic force is always perpendicular to v; a particle moving under the action of a magnetic field alone moves with a constant speed.

Motion of charged particles in a magnetic field

Motion of charged particles in a magnetic field

Fig. 27.18

Motion of charged particles in a magnetic field

Fig. 27.17

Applications of motion of charged particles Velocity Selector • Particles of a specific speed can be selected from the beam using an arrangement of electric and magnetic fields called a velocity selector.

Magnetic Force on Current Carrying Wire

FM = Il × B FM = IlB sin θ

Magnetic Force on Current Carrying Wire

Ampere’s Law • Used to determine the magnetic field yielded by currentcarrying wire • Ampere’s law states that the product B and length of line segment around any closed path equals µ0 times the net current through the area enclosed by the path. • Direction of Magnetic field is determined by corkscrew method

∑ B∆l = µ I

0 enclosed

Ampere’s Law B=µ 0I/2πL

Magnetic field profile of 2 parallel current carrying wires

Solution

µI µI µI Btotal =B1 −B2 = 0 − 0 = 0 4π d 8π d 8π d µI µI µI Btotal =B1 +B2 = 0 + 0 = 0 2π d 2π d πd µI µI µI Btotal =B2 −B1 = 0 − 0 = 0 2π d 6π d 3π d

(point P1 ) (point P2 ) (point P3 )

Magnetic Field in Solenoid

Magnetic Field in Solenoid B=µ 0nI

Ampere’s Experiment

B1=µ 0I1/2πL

F= µ 0I1I2l/2πL

Exercise

B1=µ 0I1/2πL

F/l= µ 0I1I2/2πL

Example Suspending a current with a current A horizontal wire carries a current I1=80 A dc. A second parallel wire 20 cm below it must carry how much current I2 so that it doesn’t fall due to gravity? The lower wire is a homogenous wire with a mass of 0.12 g per meter of length. F/L = mg/L=1.18 x 10-3 N/m µ 0I1I2/2π L = 1.18 x 10-3 N/m I2= 15 A

Definitions • Ampere current flowing in each of the two long parallel conductors 1 m apart, which results in a force of exactly 2 x 10-7 N/m of length of each conductor. • Coulomb one ampere-second

Solution Set

F/l= µ 0I1I2/2πL FA/l= 5.83 x 10-5N/m; 90 FB/l=3.37 x 10-5N/m; -60 FC/l=3.37 x 10-5N/m; 240