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We wish to calculate the value of eg. Two small metal conducting balls of mass m, each with charge q, are attached to massless strings of length L and suspended from the ceiling. Since the balls are both positively charged, they repel each other, and so at the ceiling the strings make an angle 0 with each other. In terms of m, q, L, 0, and g, what is en?

We wish to calculate the value of eg. Two small metal conducting balls of mass m, each with charge q, are attached to massless strings of length L and suspended from the ceiling. Since the balls are both positively charged, they repel each other, and so at the ceiling the strings make an angle 0 with each other. In terms of m, q, L, 0, and g, what is en?

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**Problem Statement: Calculating the Value of \( \epsilon_0 \)** We wish to calculate the value of \( \epsilon_0 \). Two small metal conducting balls of mass \( m \), each with charge \( q \), are attached to massless strings of length \( L \) and suspended from the ceiling. Since the balls are both positively charged, they repel each other, and so at the ceiling the strings make an angle \( \theta \) with each other. In terms of \( m \), \( q \), \( L \), \( \theta \), and \( g \), what is \( \epsilon_0 \)? **Explanation:** In this problem, we are tasked with determining the permittivity of free space, \( \epsilon_0 \), using the given parameters: - \( m \): Mass of each conducting ball - \( q \): Charge on each conducting ball - \( L \): Length of the massless strings - \( \theta \): Angle between the strings at the ceiling - \( g \): Acceleration due to gravity To approach this problem, consider the forces acting on the balls and the resulting equilibrium condition. The balls repel each other due to the like charges, creating a horizontal electrostatic force, which balances with the gravitational force acting vertically downward and the tension in the strings.
Transcribed Image Text:**Problem Statement: Calculating the Value of \( \epsilon_0 \)** We wish to calculate the value of \( \epsilon_0 \). Two small metal conducting balls of mass \( m \), each with charge \( q \), are attached to massless strings of length \( L \) and suspended from the ceiling. Since the balls are both positively charged, they repel each other, and so at the ceiling the strings make an angle \( \theta \) with each other. In terms of \( m \), \( q \), \( L \), \( \theta \), and \( g \), what is \( \epsilon_0 \)? **Explanation:** In this problem, we are tasked with determining the permittivity of free space, \( \epsilon_0 \), using the given parameters: - \( m \): Mass of each conducting ball - \( q \): Charge on each conducting ball - \( L \): Length of the massless strings - \( \theta \): Angle between the strings at the ceiling - \( g \): Acceleration due to gravity To approach this problem, consider the forces acting on the balls and the resulting equilibrium condition. The balls repel each other due to the like charges, creating a horizontal electrostatic force, which balances with the gravitational force acting vertically downward and the tension in the strings.
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