This problem is in electric charges and field chapter,

Explain the solution with diagram.

Let's dive into the topic of electric charges and fields, focusing on how to solve problems related to them. To illustrate this, I’ll walk you through a specific example involving point charges and their electric fields, along with a diagram to clarify the concepts.

Understanding Electric Charges

Electric charges can be either positive or negative. Like charges repel each other, while opposite charges attract. The fundamental unit of charge is the coulomb (C). In many problems, we deal with point charges, which are idealized charges located at a single point in space.

The Concept of Electric Field

The electric field (E) created by a point charge is a vector field that represents the force per unit charge experienced by a positive test charge placed in the field. The formula for the electric field due to a point charge (Q) at a distance (r) is given by:

E = k * |Q| / r²

where k is Coulomb's constant, approximately 8.99 x 10^9 N m²/C².

Example Problem

Let’s consider a scenario where we have two point charges: Charge Q1 = +3 µC located at the origin (0,0) and Charge Q2 = -2 µC located at (4,0) meters on the x-axis. We want to find the electric field at a point P located at (2,0) meters on the x-axis.

Step-by-Step Solution

• Calculate the electric field due to Q1 at point P:

The distance from Q1 to P is 2 meters.

Using the formula:

E1 = k * |Q1| / r1² = (8.99 x 10^9 N m²/C²) * (3 x 10^-6 C) / (2 m)²

Calculating this gives:

E1 = 6.74 x 10^3 N/C directed away from Q1 (to the right).

• Calculate the electric field due to Q2 at point P:

The distance from Q2 to P is 2 meters as well.

Using the formula:

E2 = k * |Q2| / r2² = (8.99 x 10^9 N m²/C²) * (2 x 10^-6 C) / (2 m)²

This results in:

E2 = 4.50 x 10^3 N/C directed towards Q2 (to the left).

• Determine the net electric field at point P:

Since E1 is directed to the right and E2 is directed to the left, we can find the net electric field by subtracting E2 from E1:

Net E = E1 - E2 = 6.74 x 10^3 N/C - 4.50 x 10^3 N/C = 2.24 x 10^3 N/C

The direction of the net electric field is to the right (towards Q1).

Visual Representation

To better understand this problem, let’s visualize the setup:

In the diagram, you can see Q1 and Q2 positioned on the x-axis, with point P marked in between. The arrows indicate the direction of the electric fields produced by each charge at point P.

Final Thoughts

By following these steps, you can systematically approach problems involving electric charges and fields. Remember to consider the direction of the electric fields, as they are vector quantities. This method can be applied to various configurations of charges, allowing you to analyze complex systems effectively.