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 electric field due to a uniformly charged rod.

The electric field along the axis of a uniformly charged rod is given by the equation:

E = (k * Q) / (2 * L * sqrt(r^2 + L^2))

Where:
E is the electric field in N/C,
k is the Coulomb's constant (9.0 x 10^9 N m^2/C^2),
Q is the total charge on the rod in coulombs,
L is the length of the rod, and
r is the distance from the center of the rod to the point where we want to find the electric field.

In this case:
Q = -20.0 µC = -20.0 x 10^-6 C,
L = 14.0 cm = 14.0 x 10^-2 m,
r = 36.0 cm = 36.0 x 10^-2 m.

Now, plugging these values into the equation:

E = (9.0 x 10^9 N m^2/C^2 * -20.0 x 10^-6 C) / (2 * 14.0 x 10^-2 m * sqrt((36.0 x 10^-2 m)^2 + (14.0 x 10^-2 m)^2))

Simplifying the calculation:

E = (-18 / sqrt(253))

Calculating this expression yields a value of approximately -0.113 N/C.

Thus, the magnitude of the electric field along the axis of the rod at a point 36.0 cm from its center is approximately 0.113 N/C, and the direction is negative (opposite direction to the positive charges on the rod).