# Charge ~

12

= kq

1 q

2

( r

12

)

2

ˆ

12

=

= k

Z dQ r

2

~a =

E = m

V q

|

~

D

|

= qd

——————

Charge densities

——————

Q = ρV

Q = σA

Q = λ`

1.

Charges, Forces, & Fields

E

~a k

~

D d

~ ij q i

Q r ij

ˆ ij

: Force from i on j ,

: Charge of particle

N i , C

: Charge of source particle, C

: Distance from i to j , m

: Unit vector in direction from

: Electric field, N C

1

: Energy, J

: Acceleration, ms

2

: Coulomb’s constant i to j

: Dipole moment

: Distance separating charges on dipole

2.

Electric flux and Potential

- The net flux through any closed surface surrounding a point charge independent of the shape of the surface.

q is given by

- A conductor in

· electrostatic equilibrium has the following properties :

Electric field is zero everywhere inside the conductor

·

·

Any net charge on a conductor must reside on its surface

Surface charge density is greatest where curvature is smallest q in

/ o and is

∆ V

Φ

Φ

E

E

AB

= q encl

I

ε o

=

G.S.

= kq

∆ E p

=

=

Z

A q ∆ V

B

·

1 r

A

1 r

B

· d ~ d~

Z dq

V = k r

~

{ x,y,z

}

= kq

= r

2

∂V

{ x, y, z

}

Φ

E

∆ V

AB

ε o

E p

: Electric flux, N m

2

C

1

: Change in voltage from A to B

: Permittivity constant of free space

: Potential energy, J

——————

Electric fields

—————— rod of infinite length : 2 kλ/r sheet of infinite surface : σ/ 2 o

3.

Capacitance working voltage dielectric

: Maximum safe capacitor potential difference before dielectric breakdown

: A nonconducting material whose presence between capacitor plates increases capacitance

V

E p

Q

Qd

= Ed =

=

1

2

CV

2

= CV

ε o

A

(for PPC)

(for PPC)

E

C p

E

E p

=

=

=

κ

ε o

A d

1

2

ε o

E

2

ε o

Z

E

2 dV

2

(for PPC)

V

C

=

E

( I

− e

− t/RC

) (when charging)

V

C

= V o e

− t/RC

(when discharging)

——————

Dipole shit

——————

=

τ = p

×

E p

=

~

·

V d

A

E p

C

κ

E p

E

τ

: Voltage, V

: Distance between plates of PPC,

: Surface area of one plate of PPC, m m

2

: Potential energy, J

: Capacitance, F =

: Dielectric constant

CV

1

: Electric energy density, J m

3

: Electric dipole moment for two charges of equal and opposite magnitude separated by distance ` in direction from + to

: Torque

4.

Electric current

·

·

Kirchoff ’s rules :

The sum of the currents entering any junction in a circuit must equal the sum of the currents leaving that junction.

The sum of the potential differences across all elements around any closed circuit loop must be zero.

I dQ

=

= dt nqvA

V = IR

R

J

ρ

P

ρ`

=

A

I

=

A

1

=

=

σ

IV

=

τ = RC

I n

J

τ

`

A

P

R

ρ

σ

: Current, A

: Number of charge carriers with charge velocity v passing through area A q

: Resistance, Ω

: Resistivity

: Conductivity

: Length of resistor,

: Surface area, m

2 m

: Current density

: Time constant

: Power, W and

5.

Magnetism ferromagnet paramagnet diamagnet

: Metal whose atoms’ magnetic moments are all aligned in same direction

: Substance with atoms having permanent magnetic dipole moments

: Substance whose atoms’ dipole moments are in reverse direction of field

I

τ

~

B

=

×

= + q~

× mv

2 r =

× qB f c

=

2 πm

= I~ ×

V

H

IB

= nqt

= H c

IB t

=

µ o

4 π

I Z

×

~ r

2

= max

=

=

×

·

E p

=

~

· v s

= E/B

F w

=

µ

0

I

1

I

2

`

2 πd

· d~ = µ o

I r f

~

N c

V

H n

H c

µ o

τ v s

F w s t

: Magnetic field, T

: Radius of path in magnetic field

: Cyclotron frequency

: Conductor length current direction vector

: Hall potential

: Number of charges per unit volume

: Hall coefficient

: Permeability of free space

: Torque in a current-carrying loop

: Magnetic dipole moment

: Velocity selector velocity

: Force on wire carrying carrying I

2 distance d

I

1 parallel to wire apart

: Solenoid magnetic field

: Toroid magnetic field

: Number of turns in coil

——————

I

I

S

·

Maxwell’s equations

· d ~ = d ~

ε o

= 0 q

—————— s

~ t

=

=

µ o

N I

L

µ o

N I

2 πr

S

I

I

· d~ =

− d Φ

B dt

· d~ = µ o

I + ε o

µ o d Φ

E dt

6.

Induction

Lenz’s law : The direction of an induced emf or current is such that the magnetic field created by the induced current opposes the change in magnetic flux that created the current.

L

Φ

B

E

: Inductance, V sA

1

: Magnetic flux density, T

: Induced emf, V

= kgs

2

A

1

L =

N Φ

B

I

V

L =

Φ

B

= dI/dt

Z

· d ~

E

E

I p

=

=

=

− d Φ

B dt d Φ

E

ε o

1

2

LI dt

2