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
Correct answer: B. \( T = \frac{2\pi m}{qB} \)
- A. \( T = \frac{2\pi q}{Bm} \)
- B. \( T = \frac{2\pi m}{qB} \)
- C. \( T = \frac{2\pi B}{qm} \)
- D. \( T = \frac{qB}{2\pi m} \)
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.
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Magnetic flux density and magnetic flux describe the strength of a magnetic field and the field passing through a surface. A charged particle moving through a magnetic field experiences a force perpendicular to its velocity and may follow circular or helical motion, depending on the angle between velocity and field.
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