Final answer:
To determine the magnitude and direction of the electric field along the axis of the charged rod, we can use Coulomb's law and the concept of a continuous charge distribution.
Step-by-step explanation:
To determine the magnitude and direction of the electric field along the axis of the charged rod, we can use Coulomb's law and the concept of a continuous charge distribution.
First, we need to calculate the charge per unit length of the rod. We know that the rod is 16.0 cm long and has a total charge of -25.0 µC. So, the charge per unit length (λ) can be calculated as:
λ = Total charge / Length
Substituting the values, we have:
λ = -25.0 µC / 16.0 cm
Next, we can calculate the electric field using the formula:
E = (k * λ) / (r * π)
Where k is the electrostatic constant (~9 x 10^9 N.m^2/C^2), λ is the charge per unit length, r is the distance from the center of the rod, and π is a constant (~3.14).
To find the magnitude and direction of the electric field at a point 42.0 cm from the center of the rod, substitute the values into the equation. The magnitude will be positive if the direction is away from the rod and negative if the direction is towards the rod.