When a particle of charge q and mass m enters the uniform magnetic field B moving with velocity v perpendicular to the direction of the field, the time required by a chargedparticle to make a complete revolution in a magnetic field is given by

Explanation

### Calculating Time for a Charged Particle to Complete a Revolution in a Magnetic FieldGiven:- Charge of the particle (\( q \))- Mass of the particle (\( m \))- Velocity of the particle (\( v \))- Magnetic field strength (\( B \))The formula for the time taken (\( T \)) by a charged particle to complete a revolution in a magnetic field is \( T = \frac{2\pi m}{qB} \).### Explanation of Options:#### Correct Formula:The correct formula for the time taken by a charged particle to complete a revolution in a magnetic field is \( T = \frac{2\pi m}{qB} \).#### Calculations for Correct Option:\[ T = \frac{2\pi m}{qB} \]### Explanation of Correct Option (b):The correct formula for the time taken by a charged particle to complete a revolution in a magnetic field is \( T = \frac{2\pi m}{qB} \), where \( m \) is the mass, \( q \) is the charge, and \( B \) is the magnetic field strength. This option accurately represents the relationship between mass, charge, and magnetic field strength in determining the time taken for a revolution.### Correct Answer:(b) \( T = \frac{2\pi m}{qB} \) accurately represents the time taken by a charged particle to complete a revolution in a magnetic field.