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 self-inductance
- Inside the solenoid: $$B=\mu_0nI$$
- Self-inductance: $$L=\mu_0n^2Al$$
-
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: $$ \omega_0= \gamma B_0$$
