More Applications Of Amperes Law

Concepts to remember for JEE and CBSE on More Applications of Ampere’s Law:

  • Magnetic field at centre and in between two coaxial solenoids

    • At the center: B=μ0n1I1+n2I2
    • In between: B=μ04π2n1I1r2[r2+(l/2)2]3/2
  • Solenoid: the field inside and its self-inductance

    • Inside the solenoid: B=μ0nI
    • Self-inductance: L=μ0n2Al
  • Field due to a toroid or a circular coil in the axial position and radial position:

    • On axis: B=μ04π2πNIR2xx2+R2
    • At the centre: B=μ04π2πNIR
    • At radial distance r from the axis: B=μ04π4πNIr2(R2+r2)3/2
  • Field outside a long straight wire: Solenoid (infinitely long):

B=μ0I4πr

  • Cyclotron or magnetic resonance:

    • Cyclotron’s angular frequency: ω=qeBm
    • Magnetic resonance condition: ω0=γB0