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Three particles, each of mass m and carrying a charge q each, are suspended from a common point by insulating massless strings, each of length L. If the particles are in equilibrium and are located at the corners of an equilateral triangle of side a, calculate the charge q on each particle. Assume L >>a .?
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Three particles, each of mass m and carrying a charge q each, are susp...
Equilibrium of Charged Particles in an Equilateral Triangle
In this scenario, we have three particles of mass m and charge q each, suspended from a common point by insulating massless strings of length L. The particles are in equilibrium and form an equilateral triangle of side a.
Calculating the Charge q on Each Particle
To determine the charge q on each particle, we can consider the forces acting on the particles. Since the system is in equilibrium, the electrostatic repulsive forces between the charges must balance out the gravitational forces acting on the particles.
- The repulsive force between two charges q1 and q2 separated by a distance r is given by Coulomb's Law: F = k * q1 * q2 / r^2, where k is the electrostatic constant.
- In this case, each particle experiences repulsive forces from the other two particles, forming an equilateral triangle. Let's denote the angles between the strings and the horizontal as θ.
- Resolving forces along the vertical direction, we have two components: T * sin(θ) upward (tension in the string) and 2 * k * q^2 / a^2 downward (repulsive forces from the other particles).
- Similarly, resolving forces along the horizontal direction, we have T * cos(θ) balancing out the horizontal components of the repulsive forces.
- Since the system is in equilibrium, the net force along both directions must be zero.
By solving the equations considering the equilibrium conditions and geometry of the triangle, we can determine the charge q on each particle. The details of the calculations involve trigonometry and force analysis to find the exact value of q that satisfies the equilibrium conditions.
Therefore, by carefully analyzing the forces acting on the particles and applying the principles of equilibrium, we can calculate the charge q on each particle in the system.
In this scenario, we have three particles of mass m and charge q each, suspended from a common point by insulating massless strings of length L. The particles are in equilibrium and form an equilateral triangle of side a.
Calculating the Charge q on Each Particle
To determine the charge q on each particle, we can consider the forces acting on the particles. Since the system is in equilibrium, the electrostatic repulsive forces between the charges must balance out the gravitational forces acting on the particles.
- The repulsive force between two charges q1 and q2 separated by a distance r is given by Coulomb's Law: F = k * q1 * q2 / r^2, where k is the electrostatic constant.
- In this case, each particle experiences repulsive forces from the other two particles, forming an equilateral triangle. Let's denote the angles between the strings and the horizontal as θ.
- Resolving forces along the vertical direction, we have two components: T * sin(θ) upward (tension in the string) and 2 * k * q^2 / a^2 downward (repulsive forces from the other particles).
- Similarly, resolving forces along the horizontal direction, we have T * cos(θ) balancing out the horizontal components of the repulsive forces.
- Since the system is in equilibrium, the net force along both directions must be zero.
By solving the equations considering the equilibrium conditions and geometry of the triangle, we can determine the charge q on each particle. The details of the calculations involve trigonometry and force analysis to find the exact value of q that satisfies the equilibrium conditions.
Therefore, by carefully analyzing the forces acting on the particles and applying the principles of equilibrium, we can calculate the charge q on each particle in the system.
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Three particles, each of mass m and carrying a charge q each, are suspended from a common point by insulating massless strings, each of length L. If the particles are in equilibrium and are located at the corners of an equilateral triangle of side a, calculate the charge q on each particle. Assume L >>a .?
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Three particles, each of mass m and carrying a charge q each, are suspended from a common point by insulating massless strings, each of length L. If the particles are in equilibrium and are located at the corners of an equilateral triangle of side a, calculate the charge q on each particle. Assume L >>a .? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Three particles, each of mass m and carrying a charge q each, are suspended from a common point by insulating massless strings, each of length L. If the particles are in equilibrium and are located at the corners of an equilateral triangle of side a, calculate the charge q on each particle. Assume L >>a .? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three particles, each of mass m and carrying a charge q each, are suspended from a common point by insulating massless strings, each of length L. If the particles are in equilibrium and are located at the corners of an equilateral triangle of side a, calculate the charge q on each particle. Assume L >>a .?.
Three particles, each of mass m and carrying a charge q each, are suspended from a common point by insulating massless strings, each of length L. If the particles are in equilibrium and are located at the corners of an equilateral triangle of side a, calculate the charge q on each particle. Assume L >>a .? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Three particles, each of mass m and carrying a charge q each, are suspended from a common point by insulating massless strings, each of length L. If the particles are in equilibrium and are located at the corners of an equilateral triangle of side a, calculate the charge q on each particle. Assume L >>a .? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three particles, each of mass m and carrying a charge q each, are suspended from a common point by insulating massless strings, each of length L. If the particles are in equilibrium and are located at the corners of an equilateral triangle of side a, calculate the charge q on each particle. Assume L >>a .?.
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