Final answer:
The net electric field at the center of an equilateral triangle with charged vertices will have a magnitude based on the vertical components of the individual fields due to each charge and its direction will be perpendicular to the base of the triangle, due to the cancellation of the horizontal components.
Step-by-step explanation:
To find the magnitude and direction of the net electric field due to the three charges at the center of the triangle, we must first consider the superposition principle, which states that the net electric field is the vector sum of the electric fields produced by each charge separately. In an equilateral triangle with sides of length R, the distance from each vertex to the center is (R/sqrt(3)). Using Coulomb's law, the electric field due to a point charge is given by E = k|q|/r^2, where k is Coulomb's constant, q is the charge, and r is the distance from the charge to the point of interest.
In this scenario, q1 and q2 will produce electric fields at the center pointing away from the charges since they are positive, whereas q3 will produce an electric field pointing towards it as it is negative. Because of the symmetry of the equilateral triangle and the equal magnitudes of q1, q2, and q3, the horizontal components of the electric field will cancel out. The remaining vertical component from q3 will determine the net electric field. To find the exact magnitude, we can calculate the effect of q3 and double it (since q1's and q2's vertical components add up to the effect of q3), applying E = k|q|/r^2, and to get the direction we can see it will be perpendicular to the base of the triangle, given the horizontal components cancel out.