Final answer:
To find the x-component of the electric field at point P due to charges q1 and q2, apply the electric field equation E = kQ/r² and decompose q2's field into x and y components using trigonometry. Charge q1's field affects only the y-component, not the Ex which is asked for.
Step-by-step explanation:
To calculate the x-component of the electric field (Ex) at point P due to charges q1 and q2, we must consider each charge and their respective distances from the point. The charge q1 is at the origin, and q2 is at the point (a,0), where a = 1.1m. Point P has coordinates (a,b) where b = 2.9m.
The electric field at a point due to a single point charge is given by E = kQ/r², where k is Coulomb's constant (k = 8.99 × 10⁹ Nm²/C²), Q is the charge, and r is the distance from the charge to the point in question. The x-component is found by multiplying the electric field by the cosine of the angle θ made with the x-axis, and the y-component is found by the sine of this angle.
For q1, since the charge is on the y-axis relative to point P, all its electric field will contribute to Ey (y-component), and none to Ex (x-component). For q2, the angle θ can be found using trigonometric ratios from the triangle formed by the positions of q2 and point P.
Since calculating Ey was not required and would follow a similar process, only involving different trigonometric ratios, we'll focus on finding Ex due to q2. Once θ is found, Ex can be calculated by decomposing the electric field due to q2 into it's x and y components.