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The magnetic field shown in the figure consisgs of two magnets fields. If v is the velocity just required for a charge particle of mass m and charge q to pass through the field and particle is projected with velocity v then how much time does such a charge spend in the magnetic field?
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The magnetic field shown in the figure consisgs of two magnets fields....
**Introduction**
The problem describes a magnetic field consisting of two magnets fields and asks for the time it takes for a charged particle to pass through the field. The velocity required for the particle to pass through the field is given, and the particle is projected with that velocity. We will use the principles of electromagnetic forces and motion to solve this problem.
**Given Information**
- Magnetic field consists of two magnets fields.
- Charge of the particle: q
- Mass of the particle: m
- Velocity required for the particle to pass through the field: v
**Calculating the Magnetic Force**
The magnetic force experienced by a charged particle moving in a magnetic field is given by the equation:
F = q(v x B)
Where F is the magnetic force, q is the charge of the particle, v is the velocity vector of the particle, and B is the magnetic field vector.
**Analyzing the Particle's Motion**
When a charged particle enters a magnetic field, it experiences a magnetic force perpendicular to both its velocity and the magnetic field. This force acts as a centripetal force, causing the particle to move in a circular path.
The centripetal force is given by the equation:
F = (mv^2) / r
Where m is the mass of the particle, v is its velocity, and r is the radius of the circular path.
Since the magnetic force acts as the centripetal force, we can equate the two equations:
q(v x B) = (mv^2) / r
**Solving for the Radius**
To find the radius of the circular path, we can rearrange the equation as follows:
r = (mv) / (qB)
**Calculating the Time**
The time taken for the particle to complete one full revolution is the period of its motion, which can be calculated using the formula:
T = (2πr) / v
Substituting the value of r we found earlier, we get:
T = (2π(mv) / (qB)) / v
Simplifying the expression, we have:
T = (2πm) / (qB)
**Conclusion**
The time taken for the charged particle to pass through the magnetic field is given by the equation T = (2πm) / (qB). This equation allows us to calculate the time based on the mass of the particle, its charge, and the strength of the magnetic field.
The problem describes a magnetic field consisting of two magnets fields and asks for the time it takes for a charged particle to pass through the field. The velocity required for the particle to pass through the field is given, and the particle is projected with that velocity. We will use the principles of electromagnetic forces and motion to solve this problem.
**Given Information**
- Magnetic field consists of two magnets fields.
- Charge of the particle: q
- Mass of the particle: m
- Velocity required for the particle to pass through the field: v
**Calculating the Magnetic Force**
The magnetic force experienced by a charged particle moving in a magnetic field is given by the equation:
F = q(v x B)
Where F is the magnetic force, q is the charge of the particle, v is the velocity vector of the particle, and B is the magnetic field vector.
**Analyzing the Particle's Motion**
When a charged particle enters a magnetic field, it experiences a magnetic force perpendicular to both its velocity and the magnetic field. This force acts as a centripetal force, causing the particle to move in a circular path.
The centripetal force is given by the equation:
F = (mv^2) / r
Where m is the mass of the particle, v is its velocity, and r is the radius of the circular path.
Since the magnetic force acts as the centripetal force, we can equate the two equations:
q(v x B) = (mv^2) / r
**Solving for the Radius**
To find the radius of the circular path, we can rearrange the equation as follows:
r = (mv) / (qB)
**Calculating the Time**
The time taken for the particle to complete one full revolution is the period of its motion, which can be calculated using the formula:
T = (2πr) / v
Substituting the value of r we found earlier, we get:
T = (2π(mv) / (qB)) / v
Simplifying the expression, we have:
T = (2πm) / (qB)
**Conclusion**
The time taken for the charged particle to pass through the magnetic field is given by the equation T = (2πm) / (qB). This equation allows us to calculate the time based on the mass of the particle, its charge, and the strength of the magnetic field.
Community Answer
The magnetic field shown in the figure consisgs of two magnets fields....
Πm/qB
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The magnetic field shown in the figure consisgs of two magnets fields. If v is the velocity just required for a charge particle of mass m and charge q to pass through the field and particle is projected with velocity v then how much time does such a charge spend in the magnetic field?
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The magnetic field shown in the figure consisgs of two magnets fields. If v is the velocity just required for a charge particle of mass m and charge q to pass through the field and particle is projected with velocity v then how much time does such a charge spend in the magnetic field? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The magnetic field shown in the figure consisgs of two magnets fields. If v is the velocity just required for a charge particle of mass m and charge q to pass through the field and particle is projected with velocity v then how much time does such a charge spend in the magnetic field? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The magnetic field shown in the figure consisgs of two magnets fields. If v is the velocity just required for a charge particle of mass m and charge q to pass through the field and particle is projected with velocity v then how much time does such a charge spend in the magnetic field?.
The magnetic field shown in the figure consisgs of two magnets fields. If v is the velocity just required for a charge particle of mass m and charge q to pass through the field and particle is projected with velocity v then how much time does such a charge spend in the magnetic field? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The magnetic field shown in the figure consisgs of two magnets fields. If v is the velocity just required for a charge particle of mass m and charge q to pass through the field and particle is projected with velocity v then how much time does such a charge spend in the magnetic field? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The magnetic field shown in the figure consisgs of two magnets fields. If v is the velocity just required for a charge particle of mass m and charge q to pass through the field and particle is projected with velocity v then how much time does such a charge spend in the magnetic field?.
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