Two charged particles A and B of masses (m) and ( 2m), charges ( 2q) and ( 3q ) respectively, are moving with the same velocity into a uniform magnetic field such that both particles make the same angle \( \theta (<90^\circ) \)with the direction of the magnetic field. Then the ratio of the pitches of the helical paths of the particles A and B is:
Biot-Savart’s law is an equation that gives the magnetic field produced due to a current-carrying segment. This segment is taken as a vector quantity known as the current element. In other words, Biot-Savart Law states that if a current carrying conductor of length dl produces a magnetic field dB, the force on another similar current-carrying conductor depends upon the size, orientation and length of the first current carrying element.
The equation of Biot-Savart law is given by,
\(dB = \frac{\mu_0}{4\pi} \frac{Idl sin \theta}{r^2}\)

For detailed derivation on Biot Savart Law, read more.