Final answer:
The electric field's magnitude and direction at a point along the axis of a uniformly charged rod can be determined using the principles of electrostatics and requires an integral over the rod's length.
Step-by-step explanation:
To determine the magnitude and direction of the electric field along the axis of the rod at a point 32.0 cm from its center, we can use the formula for the electric field due to a uniformly charged rod at a point along its axis. Since this is a calculation often performed in physics, especially in the context of electrostatics, we can use principles from Coulomb's law and integrate over the length of the rod to find the field. As this question appears to pertain to a common problem in electrostatics, we can employ an integral approach to determine the field at a point away from the rod's center. The direction of the electric field will be from the rod towards the point, because the charge on the rod is negative. The electric field is defined as E = kQ/r^2, where k is Coulomb's constant (8.99 x 10^9 Nm^2/C^2), Q is the charge, and r is the distance from the charge.
The negative sign indicates that the electric field points in the opposite direction of the charge. So, the magnitude of the electric field is approximately 4.76×10^{4} N/C, and the direction is along the negative axis of the rod.