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Energy gained by a charged particle is
q²B²r²/2m
Force experienced by a charged in a magnetic field
F = q (V × B )
Centripetal force provided by magnetic force. Radius =?
r = mv/qB
Angular frequency (w) omega
W = qB/m
State Biot - Savart Law
According the Biot - Savart’s Law, magnitude of magnetic field dB directly proportional to “I" ,the element length dl and inversely propor6ti r²
Biot - Savart eqn

Magnetic field at the centre of the current loop

Ampere's Circuital Law
Ampere's Circuital Law states that line integral of magnetic field B around any closed path is equal to mew knot times the total current flowing through the path
Magnetic field due to inifinitkey long straight wire
B = mew knot I/ 2 pi r
Magnetic field due to a solenoid