Final answer:
The electric field at a point on the y-axis due to two equal charges along the x-axis is found using Coulomb's Law and the principle of superposition. The horizontal components cancel each other out, and the total electric field is directed along the negative y-axis due to positive charges. A precise magnitude cannot be determined without additional information.
Step-by-step explanation:
To find the magnitude and direction of the electric field at a point on the y-axis, 0.25 m from the origin caused by two equal charges of 3.00 mc (micro-Coulombs) along the x-axis, we need to use the principle of superposition and Coulomb's Law. First, we calculate the electric field due to each charge individually at the point of interest and then vectorially add them to find the total electric field at that point.
For a point charge Q located at a distance r from a point in space, the electric field magnitude E is given by E = kQ/r², where k is Coulomb's constant, which is approximately 8.99 × 10⁹ N·m²/C².
Since the charges are the same and on the x-axis, the horizontal components of their electric fields at the point on the y-axis will cancel each other out due to symmetry. Only the vertical components will add up. The total electric field will therefore be directed along the y-axis, and due to the positive charges, it will be in the negative y-axis direction.
As the detailed calculations involve trigonometry and Coulomb's law, the precise magnitude would require more complete information. Without that information, we cannot confidently conclude which of the options (A, B, C, D) given is the correct answer.