The drawings show three charges that have the same magnitude – The drawings under examination present three charges of identical magnitude, inviting us to delve into the captivating realm of electrostatics. Coulomb’s law, a cornerstone of electromagnetism, governs the interactions between these charges, dictating the electrostatic forces that shape their behavior.
As we embark on this exploration, we will unravel the intricate interplay of electric fields, potentials, and the forces that govern the equilibrium of charged systems.
Through meticulous calculations and insightful analysis, we will uncover the electrostatic energy stored within this system and trace the work done in manipulating the charges’ positions. By shedding light on these fundamental concepts, we gain a deeper understanding of the forces that govern the behavior of charged particles, paving the way for advancements in diverse fields ranging from electronics to astrophysics.
Charges and Their Properties
Electric charge is a fundamental property of matter that determines its interactions with electric and magnetic fields. It is a scalar quantity and can be either positive or negative.
The three charges shown in the drawings have the same magnitude, but different signs. The charges are denoted as q1, q2, and q3, where q1 and q3 are positive, and q2 is negative.
Coulomb’s Law and Electrostatic Force
Coulomb’s law describes the electrostatic force between two point charges. The force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
The electrostatic force between each pair of charges in the drawings is given by:
- F12 = k – q1 – q2 / r12^2
- F23 = k – q2 – q3 / r23^2
- F31 = k – q3 – q1 / r31^2
where k is Coulomb’s constant, r12 is the distance between charges q1 and q2, r23 is the distance between charges q2 and q3, and r31 is the distance between charges q3 and q1.
Electric Field and Potential
Electric field is a vector quantity that describes the force per unit charge at a given point in space. Electric potential is a scalar quantity that describes the potential energy per unit charge at a given point in space.
The electric field due to each charge is given by:
- E1 = k – q1 / r1^2
- E2 = k – q2 / r2^2
- E3 = k – q3 / r3^2
where r1, r2, and r3 are the distances from the charges q1, q2, and q3, respectively, to the point where the electric field is being calculated.
The electric potential due to each charge is given by:
- V1 = k – q1 / r1
- V2 = k – q2 / r2
- V3 = k – q3 / r3
Net Force and Equilibrium, The drawings show three charges that have the same magnitude
The net force acting on each charge is the vector sum of the electrostatic forces due to the other charges.
For the charges in the drawings, the net force on q1 is:
F1 = F12 + F31
The net force on q2 is:
F2 = F12 + F23
The net force on q3 is:
F3 = F23 + F31
The charges are in equilibrium if the net force on each charge is zero.
Energy and Work
Electrostatic energy is the energy stored in a system of charges. The electrostatic energy of the system in the drawings is given by:
U = k – (q1 – q2 / r12 + q2 – q3 / r23 + q3 – q1 / r31)
Work is done when charges are moved from one position to another. The work done in moving the charges from their initial positions to their current positions is given by:
W = U – U0
where U0 is the electrostatic energy of the system in the initial positions.
FAQ Guide: The Drawings Show Three Charges That Have The Same Magnitude
What is the significance of the charges having the same magnitude?
The identical magnitude of the charges simplifies the analysis, allowing us to focus on the interplay of electrostatic forces without the added complexity of varying charge values.
How does Coulomb’s law govern the interactions between the charges?
Coulomb’s law quantifies the electrostatic force between any two charges, dictating the strength and direction of their interaction. It establishes the inverse square relationship between force and the distance separating the charges.
What is the relationship between electric field and electric potential?
Electric field represents the force per unit charge at a given point, while electric potential measures the work done per unit charge in moving a charge from a reference point to that location. They are interconnected through the concept of potential gradient, which relates the change in potential to the strength of the electric field.
