Answer:
The electric field can be found using Coulomb's law, which states that the force on a point charge due to a uniform distribution of charges is given by the equation:
E = k * Q / r^2
where E is the electric field, k is Coulomb's constant, Q is the total charge, and r is the distance from the point charge to the center of the distribution of charges.
In this problem, we are given that the rod is uniformly charged and has a total charge of -19.4 µC. We are also told that the distance from the point to the center of the rod is 21.8888 cm. To find the electric field, we can substitute these values into Coulomb's law:
E = (8.98755 * 10^9 Nm^2/C^2) * (-19.4 * 10^-6 C) / (21.8888 cm)^2
converting cm to m to get the units of N/C
E = (8.98755 * 10^9 Nm^2/C^2) * (-19.4 * 10^-6 C) / (0.218888 m)^2
E = -5.54717 N/C
The magnitude of the electric field along the axis of the rod at a point 21.8888 cm from the center of the rod is -5.54717 N/C.
Note that the negative sign on the answer indicates that the electric field points in the opposite direction of the distance vector.