College Physics

# Section Summary

College PhysicsSection Summary

### 22.1Magnets

• Magnetism is a subject that includes the properties of magnets, the effect of the magnetic force on moving charges and currents, and the creation of magnetic fields by currents.
• There are two types of magnetic poles, called the north magnetic pole and south magnetic pole.
• North magnetic poles are those that are attracted toward the Earth’s geographic north pole.
• Like poles repel and unlike poles attract.
• Magnetic poles always occur in pairs of north and south—it is not possible to isolate north and south poles.

### 22.2Ferromagnets and Electromagnets

• Magnetic poles always occur in pairs of north and south—it is not possible to isolate north and south poles.
• All magnetism is created by electric current.
• Ferromagnetic materials, such as iron, are those that exhibit strong magnetic effects.
• The atoms in ferromagnetic materials act like small magnets (due to currents within the atoms) and can be aligned, usually in millimeter-sized regions called domains.
• Domains can grow and align on a larger scale, producing permanent magnets. Such a material is magnetized, or induced to be magnetic.
• Above a material’s Curie temperature, thermal agitation destroys the alignment of atoms, and ferromagnetism disappears.
• Electromagnets employ electric currents to make magnetic fields, often aided by induced fields in ferromagnetic materials.

### 22.3Magnetic Fields and Magnetic Field Lines

• Magnetic fields can be pictorially represented by magnetic field lines, the properties of which are as follows:
1. The field is tangent to the magnetic field line.
2. Field strength is proportional to the line density.
3. Field lines cannot cross.
4. Field lines are continuous loops.

### 22.4Magnetic Field Strength: Force on a Moving Charge in a Magnetic Field

• Magnetic fields exert a force on a moving charge q, the magnitude of which is
$F=qvBsinθ,F=qvBsinθ, size 12{F= ital "qvB""sin"θ} {}$
where $θθ size 12{θ} {}$ is the angle between the directions of $vv size 12{v} {}$ and $BB size 12{B} {}$.
• The SI unit for magnetic field strength $BB size 12{B} {}$ is the tesla (T), which is related to other units by
$1 T=1 NC⋅m/s=1 NA⋅m.1 T=1 NC⋅m/s=1 NA⋅m.$
• The direction of the force on a moving charge is given by right hand rule 1 (RHR-1): Point the thumb of the right hand in the direction of $vv size 12{v} {}$, the fingers in the direction of $BB size 12{B} {}$, and a perpendicular to the palm points in the direction of $FF size 12{F} {}$.
• The force is perpendicular to the plane formed by $vv$ and $BB size 12{B} {}$. Since the force is zero if $vv size 12{v} {}$ is parallel to $BB size 12{B} {}$, charged particles often follow magnetic field lines rather than cross them.

### 22.5Force on a Moving Charge in a Magnetic Field: Examples and Applications

• Magnetic force can supply centripetal force and cause a charged particle to move in a circular path of radius
$r = mv qB , r = mv qB , size 12{r= { { ital "mv"} over { ital "qB"} } ,} {}$
where $vv size 12{v} {}$ is the component of the velocity perpendicular to $BB size 12{B} {}$ for a charged particle with mass $mm size 12{m} {}$ and charge $qq size 12{q} {}$.

### 22.6The Hall Effect

• The Hall effect is the creation of voltage $εε size 12{ε} {}$, known as the Hall emf, across a current-carrying conductor by a magnetic field.
• The Hall emf is given by
$ε = Blv ( B , v , and l , mutually perpendicular ) ε = Blv ( B , v , and l , mutually perpendicular ) size 12{ε= ital "Blv" $$B,v,"and"l,"mutually perpendicular"$$ } {}$
for a conductor of width $ll size 12{l} {}$ through which charges move at a speed $vv size 12{v} {}$.

### 22.7Magnetic Force on a Current-Carrying Conductor

• The magnetic force on current-carrying conductors is given by
$F=IlBsinθ,F=IlBsinθ, size 12{F= ital "IlB""sin"θ} {}$
where $II size 12{I} {}$ is the current, $ll size 12{l} {}$ is the length of a straight conductor in a uniform magnetic field $BB size 12{B} {}$, and $θθ size 12{θ} {}$ is the angle between $II size 12{I} {}$ and $BB size 12{B} {}$. The force follows RHR-1 with the thumb in the direction of $II size 12{I} {}$.

### 22.8Torque on a Current Loop: Motors and Meters

• The torque $ττ size 12{τ} {}$ on a current-carrying loop of any shape in a uniform magnetic field. is
$τ=NIABsinθ,τ=NIABsinθ, size 12{τ= ital "NIAB""sin"θ} {}$
where $NN size 12{N} {}$ is the number of turns, $II size 12{I} {}$ is the current, $AA size 12{A} {}$ is the area of the loop, $BB size 12{B} {}$ is the magnetic field strength, and $θθ size 12{θ} {}$ is the angle between the perpendicular to the loop and the magnetic field.

### 22.9Magnetic Fields Produced by Currents: Ampere’s Law

• The strength of the magnetic field created by current in a long straight wire is given by
$B = μ 0 I 2πr ( long straight wire ) , B = μ 0 I 2πr ( long straight wire ) ,$
where $II size 12{I} {}$ is the current, $rr size 12{r} {}$ is the shortest distance to the wire, and the constant $μ0=4π×10−7T⋅m/Aμ0=4π×10−7T⋅m/A size 12{μ rSub { size 8{0} } =4π times "10" rSup { size 8{ - 7} } T cdot "m/A"} {}$ is the permeability of free space.
• The direction of the magnetic field created by a long straight wire is given by right hand rule 2 (RHR-2): Point the thumb of the right hand in the direction of current, and the fingers curl in the direction of the magnetic field loops created by it.
• The magnetic field created by current following any path is the sum (or integral) of the fields due to segments along the path (magnitude and direction as for a straight wire), resulting in a general relationship between current and field known as Ampere’s law.
• The magnetic field strength at the center of a circular loop is given by
$B = μ 0 I 2R ( at center of loop ) , B = μ 0 I 2R ( at center of loop ) , size 12{B= { {μ rSub { size 8{0} } I} over {2R} } " " $$"at center of loop"$$ ,} {}$
where $RR size 12{R} {}$ is the radius of the loop. This equation becomes $B=μ0nI/(2R)B=μ0nI/(2R) size 12{B=μ rSub { size 8{0} } ital "nI"/ $$2R$$ } {}$ for a flat coil of $NN size 12{N} {}$ loops. RHR-2 gives the direction of the field about the loop. A long coil is called a solenoid.
• The magnetic field strength inside a solenoid is
$B = μ 0 nI ( inside a solenoid ) , B = μ 0 nI ( inside a solenoid ) , size 12{B=μ rSub { size 8{0} } ital "nI"" " $$"inside a solenoid"$$ ,} {}$
where $nn size 12{n} {}$ is the number of loops per unit length of the solenoid. The field inside is very uniform in magnitude and direction.

### 22.10Magnetic Force between Two Parallel Conductors

• The force between two parallel currents $I1I1 size 12{I rSub { size 8{1} } } {}$ and $I2I2 size 12{I rSub { size 8{2} } } {}$, separated by a distance $rr size 12{r} {}$, has a magnitude per unit length given by
$Fl=μ0I1I22πr.Fl=μ0I1I22πr. size 12{ { {F} over {l} } = { {μ rSub { size 8{0} } I rSub { size 8{1} } I rSub { size 8{2} } } over {2πr} } } {}$
• The force is attractive if the currents are in the same direction, repulsive if they are in opposite directions.

### 22.11More Applications of Magnetism

• Crossed (perpendicular) electric and magnetic fields act as a velocity filter, giving equal and opposite forces on any charge with velocity perpendicular to the fields and of magnitude
$v = E B . v = E B . size 12{v= { {E} over {B} } "." } {}$