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
5.2c
To determine the magnitude and direction of the electric field along the axis of the rod at a given point, we can use the formula for the electric field due to a charged rod.
The formula for the electric field at a point along the axis of a uniformly charged rod is given by:
E = (k * Q) / (L * r)
where:
E is the electric field
k is the electrostatic constant (9.0 x 10^9 N m^2/C^2)
Q is the total charge on the rod
L is the length of the rod
r is the distance between the point and the center of the rod
Given:
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 let's plug in the values and calculate the electric field:
E = (k * Q) / (L * r)
E = (9.0 x 10^9 N m^2/C^2) * (-20.0 x 10^-6 C) / (14.0 x 10^-2 m) / (36.0 x 10^-2 m)
E ≈ -0.464 N/C
Therefore, the magnitude of the electric field along the axis of the rod at a point 36.0 cm from its center is approximately 0.464 N/C. The negative sign indicates that the field is directed in the opposite direction (opposite to the positive charge).