Now suppose q2 is negative: q2 = -6 nC. What is the x-component of the net electric field at the origin?

• A. 0.947 N/C
• B. -0.947 N/C
• C. 0.385 N/C
• D. -0.385 N/C

Answer: (B)

Electric field at a point is the vector sum of the fields from all charges, and to get the x-component you project each contribution onto the x-axis and add.

For a point charge, the field at the origin points along the line from the charge to the origin, with direction away from the charge if the charge is positive and toward the charge if it is negative. The x-component of each charge’s field is found by multiplying its field magnitude by the cosine of the angle that the line to the origin makes with the x-axis (or, equivalently, by using the projection formula E_xi = - k q_i x_i / r_i^3 for charges on the x-axis, where x_i is the charge’s x-coordinate and r_i is its distance to the origin).

Now that q2 is negative, its contribution to the x-component points in the direction toward that charge, which changes the balance of the x-components. When you add the two contributions together, the x-components sum to a net value that points in the negative x-direction, giving a net x-component of -0.947 N/C. The magnitude comes from the specific distances and charges in the setup; the sign simply tells you the net field points toward negative x.