Moving charges and magnetism jee

Biot savart's law

dB=uo/4pi q(v x r)/r^3

dB= uo/4pi i(dl x r)/r^3

dB=uo/4pi idlsin/r^2

B due to current carrying straight wire
Finite wire

B=ui/4pid (costheta1 + costheta2)

Semi infinite wire

B=uoi/4pid(1+costheta2)

Infinite wire

B=uoi/2pid

B due to current carrying circular wire
Along axis

uoiR^2N/2(R^2 + X^2)^3/2
N is number of turns

At center

uoiN/2R

At centre due to arc

uoi/2R x theta/2pi

B due to solenoid

B=uoNi
At the ends: uoNi/2

Toroid

B=uo N i/2piR

Ampere's Law

B x dl = uoi
Where I is the total current crossing the area bounded by closed curve

Force on q moving in B

F = q(v x b)

Theta=0
Theta=90

F=0


F=qvB=mv^2/r
r=mv/qB
T=2pim/qb
V(frequency)= qB/2pim

If v is perpendicular to b

Circular path

r=mv/qb or root (2mk)/qB

T= 2pim/qB

W=qB/m

1 gauss is equal to how much Tesla

10^-4

Magnetic field due to straight current carrying wire

B= uoi/4pid (sintheta1 + sintheta2)

Force between parallel current carrying wires

F= uoi1i2L/2pid

Force on current carrying conductor

F=ilb

Magnetic moment

M=NiA

Torque on loop in B

Torque= M x B

Potential energy of loop in B

U=-M x B

Force on loop in b

F=M dB/dx

Motion of charge in combined magnetic and electric field

When E B and V are mutually perpendicular

V=E/B

magnetic field due to point charge with velocity

uo/4pi q( v x r)/r^3

uo/4pi value

10^-7

relationship between uo eo and c

C = 1/root uoeo