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: $$B=\mu_0 n_1 I_1+n_2 I_2$$
 In between: $$B= \frac{\mu_0}{4\pi} \frac{2n_1I_1r^2}{[r^2 +(l/2)^2]^{3/2}}$$

Solenoid: the field inside and its selfinductance
 Inside the solenoid: $$B=\mu_0nI$$
 Selfinductance: $$L=\mu_0n^2Al$$

Field due to a toroid or a circular coil in the axial position and radial position:
 On axis: $$B= \frac{\mu_0}{4\pi}\frac{2\pi NI R^2}{x\sqrt{x^2+R^2}}$$
 At the centre: $$B= \frac{\mu_0}{4\pi}\frac{2\pi NI}{R}$$
 At radial distance r from the axis: $$B= \frac{\mu_0}{4\pi}\frac{4\pi NI r^2}{\left(R^2+r^2\right)^{3/2}}$$

Field outside a long straight wire: Solenoid (infinitely long):
$$B= \frac{\mu_0 I}{4\pi r}$$

Cyclotron or magnetic resonance:
 Cyclotron’s angular frequency: $$ \omega= \frac{qeB}{m}$$
 Magnetic resonance condition: $$ \omega_0= \gamma B_0$$