The figure shows a pendulum that consists of a mass m attached to a string of length l. The mass carries charge q. Gravity points vertically down and a uniform magnetic field B, points vertically up. The potential energy of the system is?

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Answer

Understanding the Potential Energy of the Pendulum System
The potential energy of the pendulum system is influenced by both gravitational forces and the configuration of the charged mass in the presence of a magnetic field. Below is a detailed explanation of the potential energy involved.
Gravitational Potential Energy
- The gravitational potential energy (U_g) of the mass m at a height h is given by the formula:
- U_g = mgh
- Here, h can be determined from the vertical displacement of the mass when the pendulum swings.
Magnetic Potential Energy
- In a uniform magnetic field, the potential energy associated with a charged particle is not typically defined as gravitational potential energy.
- However, the interaction of the particle with the magnetic field can influence its motion and energy dynamics.
Effective Potential Energy Considerations
- The effective potential energy may account for both gravitational effects and the dynamics induced by the magnetic field.
- As the mass moves, it experiences a force due to the magnetic field, which can alter its trajectory and energy state.
Conclusion
- The total potential energy of the pendulum consists mainly of gravitational potential energy, which varies with the height of the mass.
- The magnetic field primarily influences the motion rather than contributing directly to potential energy.
- Thus, while the mass m's potential energy is primarily gravitational, its behavior is significantly affected by its charge and the magnetic field.
Understanding these aspects provides a clearer picture of the forces and energy dynamics at play in the pendulum system.

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