State Ampere's circuital law. Use this law to find the magnetic field due to a straight infinite current carrying wire. How are the magnetic field lines different from the electrostatic field lines?

Ampere's circuital law states that the line integral of magnetic field over a closed loop is μ₀ times the total current passing through the loop. That is ∮→B.d→l=μ₀I ⇒B(2πR)=μ₀I⇒B=μ₀I/(2πR)
The magnetic field lines form continuous closed loops, whereas electrostatic field lines never form closed loops.
Principle of Cyclotron- The frequency of revolution of the charged particle in a magnetic field is independent of its energy. If a particle is performing circular motion due to magnetic force then centripetal force = Magnetic force. That is, mv²/R=qvBsin90° ⇒R=mv/qB
Time period=2πR/v=2πm/qB
The time period of revolution of particles in a cyclotron is independent of their speeds. This property is necessary for the operation of a cyclotron to attain the resonance condition νa=νc where νa is the frequency of the applied voltage and νc is cyclotron frequency.