A rod 14.0 cm long is uniformly charged and has a total charge of -20.0 µC. Determine the magnitude and direction of the electric field along the axis of the rod at a point 36.0 cm from its center.

N/C

To determine the magnitude and direction of the electric field along the axis of the rod at a point 36.0 cm from its center, we can use the equation for the electric field due to a charged rod:

E = (k * Q * L) / (2 * pi * epsilon * r),

where E is the electric field, k is the Coulomb's constant (9 x 10^9 Nm^2/C^2), Q is the total charge on the rod, L is the length of the rod, epsilon is the permittivity of free space (8.85 x 10^-12 C^2/Nm^2), and r is the distance from the center of the rod to the point where the electric field is measured.

Let's plug in the given values:

Q = -20.0 µC = -20.0 x 10^-6 C,
L = 14.0 cm = 14.0 x 10^-2 m,
epsilon = 8.85 x 10^-12 C^2/Nm^2,
r = 36.0 cm = 36.0 x 10^-2 m.

Substituting these values into the equation, we have:

E = (9 x 10^9 Nm^2/C^2) * (-20.0 x 10^-6 C) * (14.0 x 10^-2 m) / (2 * pi * (8.85 x 10^-12 C^2/Nm^2) * (36.0 x 10^-2 m)).

Now, we can calculate the electric field using a calculator:

E = -2.47 x 10^7 N/C.

The magnitude of the electric field is 2.47 x 10^7 N/C, and the direction is negative (-), indicating that the electric field points in the opposite direction to the positive charge, toward the left.