moving charges and magnetism

force on a single charge

qvb sintheta

b

f/qvsintheta

f for parallel motion of mf

0

f for right angle motion of mf

qvb

radius 90

mv/qb

time period 90

2πm/qv

angular velocity 90

q/m b

f of motion at angle 0

helical

vcostheta parallel

vsintheta rotation

radius 0

mvsintheta/qb

time period 0

2πm/qb

pitch

2πm/qb vcostheta

lorrenz force

qe + qvsintheta

velocity selector

v=E/b

biosavart law

db = k idl sintheta / r²

value of k

10’-7

baxial

Mo I r² /2(r²+x²)³/²

baxial x=0

Mo I/2r

baxial x=r

Mo I/4root2a

baxial x»>a

MoIr²/2x³

ampere law

bdl = MoI

mf due to infinite long straight wire

MoI/2πr

mf inside solenoid

MonI

mf at ends of solenoid

MonI/2

mf due to inside of thick wire

MoIr/2πR²

mf due to outside of thick wire

MoI/2πr

mf on the surface of thick wire

MoI/2πr

force on a conductor

BIL sintheta

force between 2 parallel conductor

Mo I1 I2 l / 2πr

1 ampere

F= 2 × 10-⁷

force by current loop

T = mb sintheta for theta

T = mb cosetheta for alpha

mcg T

T = k phi

phi

n A B I /k

mcg I

G phi

G

k/nbA

current sensitivity

phi/I

voltage sensitivity

phi/v

G to A

Ig G = (I-Ig)S

G to V

v = Ig (G+R)

M of revolving e

evr/2

angular momentum l

mvr

M of revolving e interms of mass

le/2me

gyromagnetic ratio m/l

8.8 × 10¹⁰

bohr eqn of m for e

hen/4πme

bohr magneton value

9.27 × 10’-27