Download Electrostatics and Magnetism Equations and Concepts and more Summaries Physics in PDF only on Docsity!
Charge: 𝑞 = 𝑁 × 𝑒
Coulomb’s Law: 𝐹 = 𝑘
|
భ
||
మ
|
మ
Newton’s Law of Gravitation:
భ
మ
మ
௧௧
௩
మ
Angle between vector and x-axis:
𝛼 = tan
ି ଵ
ೣ
Electric field of test charge: 𝐸
ி
⃗
Electric field of point charge q:
మ
Parallel plate capacitor: 𝐸 =
ఌ
ఙ
ఌ
Gauss’ Law (point charge):
ఌ
(𝐸 cos 𝜃)∆𝐴 =
ொ
ఌ
௫௧
ଵ
ଶ
ଶ
ௐ
ಲಳ
ாா
ಲ
ாா
ಳ
[mechanical]
ௐ
ಲಳ
బ
ாா
ಲ
బ
ாா
ಳ
బ
ாா
∆ாா
ௐ
ಲಳ
ଵ
ଶ
ଶ
ଵ
ଶ
ଶ
ଵ
ଶ
ଶ
Point Charges: 𝑊
ಲ
ಳ
Potential of a point charge: 𝑉 =
For a parallel plate capacitor:
ௗ
ா
ா
and 𝐸 =
ா
ௗ
ఌ
ௗ
ఢ
ௗ
ଵ
ଶ
ଶ
ଵ
ଶ
ଶ
మ
ଶ
ா௬
௨
ଵ
ଶ
ଶ
∆
∆௧
[
)]
[1 + 𝛼(𝑇 − 𝑇
)]
௬
் ூ௧௩
∆
∆௧
ଶ
మ
ோ
In AC Current:
sin
sin(2𝜋𝑓𝑡)
sin
ଶ
ଵ
ଶ
ூ
√ଶ
√ଶ
௦
௦
௦
௦
௦
௦
௦
ଶ
ೝೞ
మ
ோ
In series: 𝑅
ଵ
ଶ
In parallel: 𝑅
ଵ
ோ
భ
ଵ
ோ
మ
Others & Substitutions:
ଵ
ଶ
ଶ
ଶ
Vectors:
X-component:
௫
= 𝑀 cos
Y-component:
௬
= 𝑀 sin
௫
ଶ
௬
ଶ
ୱ୧୬ ఏ
ୡ୭ୱ ఏ
= tan 𝜃
ொ
∆்
ೇ
మ
ೃ
ଵ
ଶ
ଶ
ଶ
ଶ
ା
ଶ
௦
ூ
√
ଶ
௦
√
ଶ
Terminal voltage: ∆𝑉 = 𝜀 − 𝐼𝑟
For the entire circuit: 𝜀 = 𝐼𝑅 + 𝐼𝑟
Capacitor in parallel: 𝐶 = 𝐶1 + 𝐶2 +
Capacitor in series:
ଵ
ଵ
ଵ
ଵ
ଶ
ଵ
ଷ
In RC circuits:
ௗ
ௗ௧
Charging a capacitor: 𝑞 =
ି
ೃ
ቁ
Discharging a capacitor: 𝑞 =
ି
ೃ
ி
|
|(௩ ୱ୧୬ ఏ)
magnitude of the magnetic force on the
test charge, |𝑞
| is the magnitude of the
test charge, and v is the magnitude of
the charge’s velocity.
௩
మ
௩
||
మ
ଶ
)𝐵 Where V is the voltage
The magnitude of the force that acts on
the charge moving through a magnetic
field is: 𝐹 = |𝑞|𝑣𝑏 sin 𝜃
Also 𝐹 = ቀ
∆
∆௧
(𝑣∆𝑡)𝐵 = 𝐼𝐿𝐵 sin 𝜃
(magnetic force on a current-carrying
wire of length L)
Torque:
𝑙 = 0.5𝑤 sin ∅ - where w the
width of the loop, and ∅ is the
angle between the normal to the
plane of the loop and the direction
of the magnetic field.
Circuits containing resistance,
capacitance, and inductance
்ை்
ଶ
ோ
ଶ
tan ∅ =
ಽ
ି
ೃ
ଶ
ଶ
் ை்
ଶ
ଶ
=total impedance of RLC Circuit
tan ∅ =
ಽ
ି
ோ
o With: 𝑋
= 𝐿𝜔 (in Ω) and
ଵ
ఠ
(in Ω)
CIVIL
Time Dilation: ∆𝑡 =
∆௧
బ
ට
ଵି
ೡ
మ
మ
∆𝑡
=
2 𝐷
𝑐
: proper time interval, which is the
internal between two events as measured by an
observer who is at rest with respect to the events
and who views them as occurring at the same
place.
∆𝑡: dilated time interval, which is the interval
measured by an observer who is in motion with
respect to the events and who views them as
occurring at different places.
V: relative speed between the two observers.
Length contraction: 𝐿 = 𝐿
௩
మ
మ
is the proper length
Magnitude of the relativistic
momentum: 𝑝 =
௩
ට
ଵି
ೡ
మ
మ
Total energy of an object: 𝐸 =
మ
ට ଵି
ೡ
మ
మ
Kinetic energy of an object:
ଶ
ଶ
ଶ
ଶ
ଶ
ଶ
ଶ
ସ
Velocity addition:
ଶ
Energy of a proton: 𝐸 = ℎ
𝝀
௫
Compton effect: hf (energy of
incident photon) = hf’ (energy of
scattered photon) +KE (kinetic energy
of recoil electron
For an initially stationary electron:
- 𝑝⃗ (momentum of incident photon) = 𝑝′
(momentum of
scattered photon) + 𝑝⃗
௧
(momentum of recoil
electron)
ா
𝝀
𝝀
ᇱ
(1 − cos 𝜃)
Where
is the Compton wavelength of the electron
and 𝜃 is the angle between axis of electron and the
scattered wavelength
Heisenberg Uncertainty Principle
௬
ௐ
where w is the width of the slit
௬
ସగ
(momentum and position)
ସగ
(energy and time)
Where:
): uncertainty in the y component of the linear momentum of
the particle.
- (∆𝑦): uncertainty in a particle’s position along the y direction
- (∆𝐸): uncertainty in the energy of a particle when the particle is
in a certain state
- (∆𝑡): time interval during which the particle is in the state.
- Lyman series:
ଵ
ఒ
ଵ
ଵ
మ
ଵ
మ
ଵ
ఒ
ଵ
ଶ
మ
ଵ
మ
ଵ
ఒ
ଵ
ଷ
మ
ଵ
మ
- The magnitude of the orbital
angular momentum: 𝐿
ଶగ
- Radius of nth Bohr orbit: 𝑟
(5.29 × 10
ିଵଵ
మ
మ
మ
ଵ
ఒ
ଵ
మ
ଵ
మ
) where 𝑛
- Minimum wavelength of X-Ray:
