In figure 1 charge q2 experiences no net electric force – In the realm of electrostatics, Coulomb’s Law reigns supreme, dictating the interactions between electric charges. In Figure 1, we encounter a captivating scenario where charge Q2 stands apart, experiencing no net electric force. This intriguing phenomenon sparks our curiosity, inviting us to delve into the intricate interplay of electric forces and fields that govern this enigmatic behavior.
Coulomb’s Law, with its mathematical precision, quantifies the strength and direction of the electric force between two point charges. It reveals the inverse square relationship between force and distance, highlighting the profound influence of charge magnitude and separation. In Figure 1, we witness the delicate balance of forces acting upon charge Q2, resulting in a net force of zero.
Coulomb’s Law and Net Electric Force: In Figure 1 Charge Q2 Experiences No Net Electric Force
Coulomb’s Law describes the electrostatic force between two charged particles. It states that the force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. Mathematically, it can be expressed as:
F = k
- (q1
- q2) / r^2
where:
- F is the electrostatic force in newtons (N)
- k is Coulomb’s constant, approximately 8.988 x 10^9 N m^2/C^2
- q1 and q2 are the charges of the particles in coulombs (C)
- r is the distance between the particles in meters (m)
Net Electric Force
The net electric force on a charge is the vector sum of all the electric forces acting on it. The magnitude of the net electric force is given by:
F_net = |F_1| + |F_2| + … + |F_n|
where:
- F_net is the net electric force in newtons (N)
- F_1, F_2, …, F_n are the individual electric forces in newtons (N)
The direction of the net electric force is determined by the vector sum of the individual electric forces.
In Figure 1, charge Q2 experiences no net electric force because the electric forces exerted by charges Q1 and Q3 cancel each other out.
Electric Field
An electric field is a region of space around a charged particle where other charged particles experience an electric force. The electric field is defined as the force per unit charge at a given point in space:
E = F / q
where:
- E is the electric field in newtons per coulomb (N/C)
- F is the electric force in newtons (N)
- q is the charge in coulombs (C)
In Figure 1, charge Q1 creates an electric field that points away from it, while charge Q3 creates an electric field that points towards it. The net electric field at the location of charge Q2 is zero because the electric fields of Q1 and Q3 cancel each other out.
Superposition Principle, In figure 1 charge q2 experiences no net electric force
The superposition principle states that the net electric field at a point in space due to multiple charges is the vector sum of the electric fields due to each individual charge. Mathematically, it can be expressed as:
E_net = E_1 + E_2 + … + E_n
where:
- E_net is the net electric field in newtons per coulomb (N/C)
- E_1, E_2, …, E_n are the electric fields due to each individual charge in newtons per coulomb (N/C)
The superposition principle can be used to calculate the net electric force on charge Q2 in Figure 1. The electric field at the location of Q2 due to Q1 is given by:
E_1 = k
q1 / r_1^2
where r_1 is the distance between Q1 and Q2.
The electric field at the location of Q2 due to Q3 is given by:
E_3 = k
q3 / r_3^2
where r_3 is the distance between Q3 and Q2.
The net electric field at the location of Q2 is given by:
E_net = E_1 + E_3 = k
- q1 / r_1^2 + k
- q3 / r_3^2
The net electric force on Q2 is given by:
F_net = q2
- E_net = q2
- (k
- q1 / r_1^2 + k
- q3 / r_3^2)
Since the net electric field at the location of Q2 is zero, the net electric force on Q2 is also zero.
The superposition principle can be applied to any situation involving multiple charged particles.
FAQ Resource
Why does charge Q2 experience no net electric force in Figure 1?
In Figure 1, the electric forces exerted on charge Q2 by charges Q1 and Q3 cancel each other out, resulting in a net force of zero.
How does Coulomb’s Law contribute to understanding the scenario in Figure 1?
Coulomb’s Law provides the mathematical framework for calculating the electric force between charges Q1, Q2, and Q3, allowing us to determine the magnitude and direction of each force.
What is the significance of the superposition principle in analyzing Figure 1?
The superposition principle enables us to calculate the net electric force on Q2 by considering the individual forces exerted by Q1 and Q3, even though they act simultaneously.
