# Formula Sheet – PHY 162 – Exam C

```Formula Sheet – PHY 162 – Exam C
Chapter 21: Electric Charge
Coulomb’s Force Law: ⃗
̂
Total electric force: ⃗
⃗
⃗
⃗
⃗
Electrostatic constant:
Permittivity constant:
Electric current:
Charge quantization:
; where
and the electron charge is – .
Chapter 22: Electric Fields
Definition: ⃗⃗
⃗
, or ⃗
⃗⃗
Electric field lines: At any point, ⃗⃗ is tangent to the line through that point. The
magnitude of ⃗⃗ is proportional to the number of lines per unit area.
Point charge (Coulomb’s Law): ⃗⃗
Total electric field at a point: ⃗⃗
Electric dipole moment: ⃗
along the z axis at
̂
⃗⃗
⃗
⃗⃗
⃗⃗
̂ where two charges of charge &plusmn;q are placed
.
Electric dipole field
Along the z axis (z&raquo;d): ⃗⃗
̂ , in the +z direction.
| |
Along the x axis (x&raquo;d): ⃗⃗
̂ , in the -z direction.
| |
Electric dipole in external field
Torque: ⃗ ⃗ ⃗⃗ , Potential energy:
⃗ ⃗⃗
Chapter 23: Gauss’ Law
Flux of electric field through surface:
∮ ⃗⃗ ⃗⃗⃗⃗⃗⃗
⃗⃗ ∮ ⃗⃗⃗⃗⃗⃗
Flat surface and constant field:
∮
Constant field perpendicular to the surface:
Gauss’ Law:
⁄
∮
, or
Charged isolated conductor:
Cylindrical symmetry: ( )
Planar symmetry:
⃗
⃗⃗
⁄
( )
⁄(
just outside,
)
⁄
Spherical symmetry: ( )
( )
⁄(
)
inside
Ch 24 Electric Potential
Electric potential energy:
forces.
Electric potential:
then
.
, where
(
)
Uniform electric field: Since
. Units: [ ]
Electron-volt (
):
is the work done by all electric
. If the potential is zero at infinity,
(
(
, we have
) [ ]
)(
For an arbitrary electric field, we have is
, and
)
∫ ⃗⃗
⃗ and
component form this is
Point Charge:
⃗⃗
⃗⃗
⃗⃗. In
.
. For two or more charges,
∑
.
Electric dipole:
, where is the dipole moment, is the
distance from the dipole center, and is measured from the dipole axis.
Electric potential energy: Two charges have
For a set of charges,
∑
Charged isolated conducting sphere of radius
electric field at the surface is
and charge :
The
Chapter 28: Magnetic Fields
Magnetic field ⃗⃗ defined by the Lorentz force: ⃗
Units: [ ]
(
)
⃗
⃗⃗,
| |
,
(Tesla).
Crossed fields: Particle passes if
Uniform circular motion:
.
Magnetic force on a wire with current : ⃗
⃗⃗
⃗⃗ ,
Magnetic dipole moment of a current loop:
Magnetic dipole in external field
Potential energy:
⃗ ⃗⃗ ; Torque: ⃗
⃗
⃗⃗ .
.
Chapter 29: Magnetic Fields due to Currents
4 x 10-7 Tm/A
Vacuum permeability constant:
(Biot-Savart Law) Magnetic field generated by a current: ⃗⃗
Long straight wire:
(
) , Circular arc of wire:
∫ ⃗⃗,
(
( )
⃗
⃗
) , attractive if in the same
direction, repulsive if in opposite directions.
Ampere’s Law: ∮ ⃗⃗
⃗
.
Long straight wire of radius :
Outside (
):
;
):
( )
.
Ideal solenoid:
, inside where
;
Inside (
Ideal toroid:
, inside;
Magnetic field far along axis of a coil:
.
).
(
Force between two parallel currents:
⃗⃗
, outside.
, outside.
.
```