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A charged particle of mass m1 and charge q1 is revolving in a circle of radius r. Another charged particle of charge q2 and mass m2 is situated at the centre of of the circle. If the velocity and time period of the revolving particle be v and T respectively then.?
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A charged particle of mass m1 and charge q1 is revolving in a circle o...
Centripetal Force and Equations of Motion:
When a charged particle of mass m1 and charge q1 revolves in a circle of radius r, it experiences a centripetal force towards the center of the circle. This centripetal force is provided by the electrostatic force of attraction between the revolving particle and the particle at the center.
The electrostatic force between two charged particles is given by Coulomb's Law:
F = k * (|q1*q2|/r^2)
Where F is the force, k is the electrostatic constant, q1 and q2 are the charges of the particles, and r is the distance between them.
Centripetal Force and Electrostatic Force:
In this case, the electrostatic force is acting as the centripetal force. Therefore, we can equate the two forces:
F = m1 * (v^2/r) (1)
Where m1 is the mass of the revolving particle and v is its velocity.
Substituting the expression for the electrostatic force in equation (1), we get:
k * (|q1*q2|/r^2) = m1 * (v^2/r)
Simplifying the equation, we find:
v^2 = (k * |q1*q2| * r) / m1
Time Period:
The time period (T) of the revolving particle is the time taken to complete one revolution around the circle. It is related to the velocity and the circumference (2πr) of the circle as:
T = (2πr) / v
Relationship between Time Period and Velocity:
We can substitute the value of v^2 from the previous equation into the expression for time period:
T = (2πr) / sqrt((k * |q1*q2| * r) / m1)
Simplifying further, we get:
T = 2π * sqrt((m1 * r^3) / (k * |q1*q2|))
Conclusion:
In conclusion, the velocity of the revolving particle is given by v = sqrt((k * |q1*q2| * r) / m1), and the time period is given by T = 2π * sqrt((m1 * r^3) / (k * |q1*q2|)). These equations describe the relationship between the velocity, time period, mass, charge, and radius of the revolving particle.
When a charged particle of mass m1 and charge q1 revolves in a circle of radius r, it experiences a centripetal force towards the center of the circle. This centripetal force is provided by the electrostatic force of attraction between the revolving particle and the particle at the center.
The electrostatic force between two charged particles is given by Coulomb's Law:
F = k * (|q1*q2|/r^2)
Where F is the force, k is the electrostatic constant, q1 and q2 are the charges of the particles, and r is the distance between them.
Centripetal Force and Electrostatic Force:
In this case, the electrostatic force is acting as the centripetal force. Therefore, we can equate the two forces:
F = m1 * (v^2/r) (1)
Where m1 is the mass of the revolving particle and v is its velocity.
Substituting the expression for the electrostatic force in equation (1), we get:
k * (|q1*q2|/r^2) = m1 * (v^2/r)
Simplifying the equation, we find:
v^2 = (k * |q1*q2| * r) / m1
Time Period:
The time period (T) of the revolving particle is the time taken to complete one revolution around the circle. It is related to the velocity and the circumference (2πr) of the circle as:
T = (2πr) / v
Relationship between Time Period and Velocity:
We can substitute the value of v^2 from the previous equation into the expression for time period:
T = (2πr) / sqrt((k * |q1*q2| * r) / m1)
Simplifying further, we get:
T = 2π * sqrt((m1 * r^3) / (k * |q1*q2|))
Conclusion:
In conclusion, the velocity of the revolving particle is given by v = sqrt((k * |q1*q2| * r) / m1), and the time period is given by T = 2π * sqrt((m1 * r^3) / (k * |q1*q2|)). These equations describe the relationship between the velocity, time period, mass, charge, and radius of the revolving particle.
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A charged particle of mass m1 and charge q1 is revolving in a circle of radius r. Another charged particle of charge q2 and mass m2 is situated at the centre of of the circle. If the velocity and time period of the revolving particle be v and T respectively then.?
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A charged particle of mass m1 and charge q1 is revolving in a circle of radius r. Another charged particle of charge q2 and mass m2 is situated at the centre of of the circle. If the velocity and time period of the revolving particle be v and T respectively then.? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A charged particle of mass m1 and charge q1 is revolving in a circle of radius r. Another charged particle of charge q2 and mass m2 is situated at the centre of of the circle. If the velocity and time period of the revolving particle be v and T respectively then.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A charged particle of mass m1 and charge q1 is revolving in a circle of radius r. Another charged particle of charge q2 and mass m2 is situated at the centre of of the circle. If the velocity and time period of the revolving particle be v and T respectively then.?.
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