Three charges are positioned as indicated in the figure – Three charges positioned as indicated in the figure present a captivating scenario in electrostatics, where the arrangement of charges orchestrates a symphony of forces, interactions, and energy transformations. This intricate interplay holds profound significance, influencing electric fields, dictating charge dynamics, and paving the way for practical applications.
As we delve into the intricacies of this configuration, we will unravel the forces governing each charge, explore the interplay between them, and uncover the profound implications for potential energy and electric potential. Moreover, we will venture into the realm of real-world applications, showcasing how this arrangement of charges finds practical expression in various devices and systems.
Three Charges
Three charges, q1, q2, and q3, are positioned as indicated in the figure. The charges form an equilateral triangle with side length ‘a’.
The significance of this arrangement is that it creates a unique electric field and interactions between the charges.
Force and Interactions, Three charges are positioned as indicated in the figure
- The force acting on q1 due to q2 and q3 is given by:
- F12 = k – q1 – q2 / a^2
- F13 = k – q1 – q3 / a^2
The forces F12 and F13 are equal in magnitude but opposite in direction, resulting in a net force of zero on q1.
Similarly, the net force on q2 and q3 is also zero.
Potential Energy and Electric Potential
- The potential energy of the system of charges is given by:
- U = k – (q1 – q2 / a + q1 – q3 / a + q2 – q3 / a)
The electric potential at a point due to the three charges is given by:
Applications
- The arrangement of three charges is used in various applications, such as:
- Electric field sensors
- Ion traps
- Particle accelerators
FAQ Overview: Three Charges Are Positioned As Indicated In The Figure
What is the significance of the arrangement of three charges?
The arrangement of three charges determines the magnitude and direction of the forces acting on each charge. It also influences the electric field created by the charges and the potential energy of the system.
How do the charges interact with each other?
The charges interact through electrostatic forces. Like charges repel each other, while unlike charges attract each other. The strength and direction of these forces depend on the magnitude of the charges and the distance between them.
What is the relationship between potential energy and electric potential?
Potential energy is the energy stored in a system due to the arrangement of charges. Electric potential is the potential energy per unit charge. The potential energy of a system of charges is directly proportional to the electric potential.
