Electricity and Magnetism Formula Sheet & study guide Physics A

Parallel oppositely charged plates

UNIFORM

- I|I|+ →

CONVENTIONAL CURRENT pos → neg

Type equation here.

Electrons

𝑱𝒖𝒏𝒄𝒕𝒊𝒐𝒏 𝑳𝒂𝒘 𝑰𝟏 = 𝑰𝟐 + 𝑰𝟑

INDUCTION

𝑹𝑬𝑺𝑰𝑺𝑻𝑶𝑹𝑺 𝑰𝑵 𝑺𝑬𝑹𝑰𝑬𝑺

𝑅𝑇 = 𝑅1 + 𝑅2 + 𝑅3 + 𝑅4 . .

𝐞 = −𝟏. 𝟔 × 𝟏𝟎−𝟏𝟗 𝐜oloumbs (c) 𝐞 = 𝟗. 𝟏𝟏 × 𝟏𝟎−𝟑𝟏 𝐊𝐠

𝐄 𝐕𝐦 −𝟏 =

𝟏 𝐜𝐨𝐥𝐨𝐮𝐦𝐛 = 𝟔. 𝟐𝟓 × 𝟏𝟎𝟏𝟖 𝐞

𝐕 = 𝐄𝐝 = 𝐤𝐐𝟏 𝐐𝟐

= qE

𝐝𝟐

Coulombs Law

𝐅𝐞 =

Fe= force between the 2 objects K= constant= 𝟗 × 𝟏𝟎𝟗

𝑵𝒎 𝒄𝟐

𝑸𝟏 &𝑸𝟐 =charge of object 1 & 2 (C)

𝐅𝐞 =

1 𝑅𝑇

𝐰 𝐪

𝐤𝐐𝟏 𝐐𝟐 = 𝐪𝐄 𝐝𝟐 𝐚= 𝐝 𝐯

Lower Resistance = Thicker Filament

𝟏

𝐬 = 𝐮𝐭 + 𝟐𝐚𝐭 𝟐

𝟐𝐪𝐄𝐬 = 𝐦

𝟐𝐅𝐞 𝐬 𝐦

𝐏𝐎𝐖𝐄𝐑 (𝐖𝐚𝐭𝐭𝐬) 𝐑𝐚𝐭𝐞 𝐨𝐟 𝐞𝐧𝐞𝐫𝐠𝐲 𝐭𝐫𝐚𝐧𝐬𝐟𝐞𝐫 𝐏=

𝐄nergy(𝐰) 𝐪𝐕 𝐕𝟐 = = 𝐈𝐕 = = 𝐈𝟐 𝐑 𝐭 𝐭 𝐑

𝐑=

𝐏 𝐪𝐕 𝐕 𝟐 𝐕 𝟐 𝐭 𝐰 𝐕𝐭 𝐕 = = = = 𝟐= = 𝐈 𝟐 𝐭𝐈 𝟐 𝐏 𝐰 𝐭𝐈 𝐪 𝐈

𝐈=

𝐏 𝐰 𝐪 𝐂 𝐏 𝐪𝐕 𝐕 = = = =± 𝐨𝐫 = 𝐕 𝐭𝐕 𝐭 𝐬 𝐑 𝐭𝐑 𝐑

𝐅𝐞 = 𝐄𝐪 = 𝐅𝐰 = 𝐦𝐠 𝐦𝐠 𝐄

ELECTRON GUN

𝐅𝐞 𝐪

=

𝐤𝐐 𝐝𝟐

=

𝐍 𝐂

𝐕

𝑎𝑙𝑠𝑜 𝐄 = 𝐕 𝐦 = 𝐝

𝐅𝐞 = 𝐪𝐄 −𝟏

𝐄 = electric field strength (𝐍/𝐜)(𝐍𝐂 )(𝐕 𝐦) In the same direction as Fe if Q is positive Electric Potential near point charge Q

𝐤𝐐 𝐝𝟏

𝐕𝟐 =

Potential V of surface of a sphere

𝐤𝐐 𝐝𝟐

V=

kQ r

ELECTRIC POTENTIAL DIFFERENCE (Work (Joules) needed to move charge between 2 points

𝐰 𝐉oules 𝐍𝐦 ∆𝐕 = = = = 𝑽𝟐 − 𝑽𝟏 = 𝐄𝐝 𝐪 𝐂oloumb 𝐂 𝐕 𝐍 𝐇𝐄𝐍𝐂𝐄 = =𝐄 𝐦 𝐂 𝟏 𝐄𝐍𝐄𝐑𝐆𝐘 𝐌𝐄𝐓𝐇𝐎𝐃 𝐖 = 𝐪𝐕 = 𝐪𝐄𝐝 = 𝐦𝐯 𝟐 𝟐

𝐈=

𝐕 𝐑

𝐕=

𝟐 × 𝐪𝐞 × 𝐕 𝐦

𝐪

= = 𝐧𝐪𝐯 𝐭

𝐏𝐨𝐰𝐞𝐫 𝐢𝐧 𝐏𝐨𝐰𝐞𝐫 𝐨𝐮𝐭

× 𝟏𝟎𝟎

𝐕 𝐕𝐭 𝐕 = = 𝐈 𝐪 𝐧𝐪𝐯

𝐈 = Electric current (𝐀𝐦𝐩𝐬) (rate of flow of charges with time) R= Resistance of wire (Ohms)(Ω)=(Volt/amp) Dependant on temperature T ↑ R ↑ 𝐕 = 𝐄𝐌𝐅 voltage − the force moving e (𝐕) (𝐉/𝐜)

𝐯 = e drift velocity (𝐦 𝐬) 𝒏 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑒 𝑝𝑒𝑟 𝑚𝑒𝑡𝑟𝑒 R∝L

𝐕𝟐𝐭 𝟏 = 𝐈 𝟐 𝐑𝐭 = 𝐏𝐭 = 𝐈𝐕𝐭 = 𝟐𝐦𝐯 𝟐 𝐑

𝐄𝐟𝐟𝐢𝐜𝐢𝐞𝐧𝐜𝐲 =

𝐪𝐑 𝐕 = 𝐈𝐑 = = 𝐧𝐪𝐯𝐑 = 𝐄𝐌𝐅 𝐭 𝐑=

𝐏 𝐏𝐭 𝐰 𝐰 𝐉 𝐍𝐦 𝐪𝐑 = = = = = = ± 𝐑𝐏 = = 𝐈𝐑 𝐈 𝐪 𝐭𝐈 𝐪 𝐂 𝐂 𝐭

𝐖 = 𝐪𝐕 =

FOR A PARTICULAR METAL

𝐕𝟏 =

𝐦𝐯 𝟐 𝐪𝐞 × 𝐕 = ⟹𝐯= 𝟐

Ohm’s Law

𝐄=

3

𝑽 = 𝑽𝟏 + 𝑽𝟐 + 𝑽𝟑

𝐅𝐞 𝐪𝐄 = 𝐦 𝐦

MILIKANS LAW (in suspension)

𝐪=

1

2

𝑽 − 𝑽𝟏 + 𝑽𝟐 + 𝑽𝟑 = 𝟎

𝟐

𝒗 = 𝟐𝒂𝒔 =

1

1

𝐋𝐨𝐨𝐩 𝐋𝐚𝐰

𝐅𝐎𝐑𝐂𝐄 𝐌𝐄𝐓𝐇𝐎𝐃

Electric Field Strength Force per coloumb exerted on a test charge at that point

1

= 𝑅 + 𝑅 + 𝑅 +. .

𝐰 = 𝐪𝐞𝐝

𝐯 𝟐 = 𝐮𝟐 + 𝟐𝐚𝐬 𝐭 =

𝐒𝐮𝐫𝐟𝐚𝐜𝐞 𝐀𝐫𝐞𝐚 𝐨𝐟 𝐚 𝐬𝐩𝐡𝐞𝐫𝐞 = 𝟒𝛑𝐫

𝑹𝑬𝑺𝑰𝑺𝑻𝑶𝑹𝑺 𝑰𝑵 𝑷𝑨𝑹𝑨𝑳𝑳𝑬𝑳

𝐕𝐨𝐥𝐭𝐬 𝐕 𝐅𝐞 𝐤𝐐 = = = 𝟐 𝐦𝐞𝐭𝐫𝐞 𝐝 𝐪 𝐝

𝐈𝐌 ≤ 𝐟𝐬𝐝 R S = Shunt resistor (𝐋𝐎𝐖 𝐑) IS × R s = IM × R M 𝐼𝑡𝑜𝑡 = 𝐼𝑆 + 𝐼𝑀 I ×R M

L R∝ A

𝐋 𝐑=𝐩 𝐀

RS = I M

tot −I M

𝐩 = Resistivity of wire (Ω/𝐦) 𝐋 = Length of wire 𝐀 = cross sectional area = 𝝅𝒓𝟐

𝐯=

𝟐𝐪𝐕 𝐦 𝑽 𝑰

=𝑹 R s = series resistor (𝐇𝐈𝐆𝐇 𝐑) 𝑉 = 𝐼𝑀 × (𝑅𝑆 + 𝑅𝑀 )

CURRENT CARRYING WIRE IN A MAGNETIC FIELD

ELECTROMAGNETIC INDUCTION Potential difference (∆𝐕) (𝐄𝐌𝐅) induced across a conductor in or moving thru a magnetic field B

𝑷𝑨𝑹𝑨𝑳𝑳𝑬𝑳 𝑪𝑶𝑵𝑫𝑼𝑪𝑻𝑶𝑹𝑺 𝑪𝑨𝑹𝑹𝒀𝑰𝑵𝑮 𝑨 𝑪𝑼𝑹𝑹𝑬𝑵𝑻 A

B

𝐅𝐁 =

𝐤′𝐈𝟏 𝐈𝟐𝐋 𝐝

𝐈𝟏 𝐈𝟐 = current in each wire

𝐅 = 𝐁𝐪𝐯 𝐬𝐢𝐧 𝛝

𝐋 = Length of each wire

𝐖 = 𝐅 × 𝐋 = 𝐪𝐯𝐁𝐬𝐢𝐧𝛉 × 𝐋 𝐃 = distance separating the wires

W = p. d.× q = EMF × q

𝐤’ = 2 × 10−7 A-Attractive force

𝐅𝐁 = 𝐁𝐈𝐋 𝐬𝐢𝐧 𝛝

B-Repulsive force

𝐄𝐌𝐅 = ∆𝐕 =

𝐖 = 𝐁𝐋𝐯 𝐬𝐢𝐧 𝛉 𝐪

∆V = EL or E =

∆V = vB so ∆V = EMF = vLB L

𝐈 = current (𝐀) 𝐁 = magnetic field strength 𝐌𝐚𝐠𝐧𝐞𝐭𝐢𝐜 𝐟𝐢𝐞𝐥𝐝 𝐬𝐭𝐫𝐞𝐧𝐠𝐭𝐡 − (𝑻) 𝑾/𝒎𝟐

𝐁=

𝐤′𝐈 𝐝

∆V L

𝐋 = Length of conductor within the magnetic field 𝛉 = angle between the conductor and magnetic field

𝐄𝐌𝐅 = ∆𝐕 = 𝐁𝐋𝐯 𝐬𝐢𝐧 𝛉

Mass Spectrometer MOVING CHARGES IN MAGNETIC FIELDS

I= electric current in wire d= distance from the wire 𝐤’ = 2 × 10−7 𝐁 = magnitude of magetic field strength 𝑴𝒂𝒈𝒏𝒆𝒕𝒊𝒄 𝒇𝒊𝒆𝒍𝒅 𝒔𝒕𝒓𝒆𝒏𝒈𝒕𝒉 𝒊𝒏 𝒂 𝒄𝒊𝒓𝒄𝒖𝒍𝒂𝒓 𝒍𝒐𝒐𝒑

𝑩=

𝐅𝐁 =

𝝅𝒌′𝑰 𝒓

𝐅𝐁 = 𝐅𝐂

r= radius of loop 𝐁′ for current in a 𝐒𝐨𝐥𝐞𝐧𝐨𝐢𝐝 (UNIFORM)

𝐁=

𝐁𝐪𝐋 = 𝐁𝐪𝐯 𝐬𝐢𝐧 𝛝 𝐓 𝐁𝐪𝐯 𝐬𝐢𝐧 𝛝 = 𝐫=

𝐦𝐯 𝟐 𝐫

𝐦𝐯 𝐪𝐁

𝟐𝛑𝐤′𝐍𝐈 𝐋

𝐬=

𝟐𝐚 𝐮+𝐯 𝟐

𝐱𝐭

v = u + at 𝐚=

𝐯−𝐮 𝐭

𝐦𝐯 𝟐 = 𝐪𝐯𝐁 𝐫

Mark Riley [email protected]

𝐪𝐁 𝟐 𝐫 𝟐 𝟐𝐕

BCOME(+) Low Affinity for 𝑒 Rabbit cat fur Acetate Perspex Glass Wool Lead Silk Paraffin wax Polythene Ebonite Copper Rubber Amber Sulfur Gold BCOME(-) High Affinity for 𝑒

Triboelectric Series

𝐬=

𝐯𝟐− 𝐮𝟐

𝐪𝐁𝟐 𝐫 𝟐 𝟐𝐕

The Centripetal force is provided by the magnetic force 𝐅𝐜 = 𝐅𝐁 𝐦𝐯 𝟐 𝐅𝐜 = & 𝐅𝐁 = 𝐪𝐯𝐁 𝐫

𝐦=

𝐋 = Length of solenoid 𝐍 = number of turns or loops

𝐁 = magnetic field strength 𝐋 = Length of conductor within the magnetic field 𝛉 = angle between the conductor and magnetic field

𝐦=