Main Answer:
The point to the left of q1 where the electric field is zero is located at approximately 10 cm from q1.
Step-by-step explanation:
To identify the specific location where the electric field becomes zero due to the interaction of two point charges, q1 = -28 μC and q2 = 42 μC, placed 15 cm apart along the x-axis, the application of the superposition principle is paramount.
The superposition principle, a fundamental concept in electromagnetism, posits that the net electric field at any point is the vector sum of individual electric fields produced by each charge in the system.
In this configuration, q1 and q2 generate electric fields with opposite directions; the field from q1 extends outward, while the field from q2 points inward. The critical point where these electric fields cancel each other out is the precise location sought.
Coulomb's law, expressed as E = k * q / r^2, where k is Coulomb's constant, q is the charge, and r is the distance, serves as the mathematical foundation for determining the magnitudes of the electric fields from q1 and q2.
By equating the magnitudes of these electric fields and solving for the distance, it is established that the point where the electric fields nullify each other is situated at a distance of approximately 10 cm from q1.
This result signifies that at this specific location, the electric field produced by q1 equals in magnitude but opposes in direction to that generated by q2, leading to a net electric field of zero.
A solid grasp of these foundational principles is essential for understanding the intricate dynamics of electric fields in diverse charge configurations.