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 Coulomb's law.
Coulomb's law states that the electric field (E) due to a uniformly charged rod at a particular point along its axis 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 of the rod, L is the length of the rod, and r is the distance between the point and the center of the rod along its axis.
Given:
Q = -20.0 µC (negative charge indicates excess of electrons)
L = 14.0 cm
r = 36.0 cm
First, we need to convert the given values to SI units:
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, we can substitute these values into the formula 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))
Calculating this expression, we get:
E ≈ -7.68 x 10^5 N/C
The negative sign indicates that the electric field is directed in the opposite direction to that of the positive charges. Therefore, the direction of the electric field along the axis of the rod at a point 36.0 cm from its center is opposite to the direction away from the rod.