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
toward the rod
away from the rod
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, you can use the formula for electric field due to a uniformly charged rod:
E = (k * q * x) / (L^2 * sqrt((L/2)^2 + x^2))
Where:
E is the electric field
k is the Coulomb's constant (k = 9 * 10^9 N m^2/C^2)
q is the total charge on the rod (-20.0 µC = -20.0 * 10^-6 C)
x is the distance from the center of the rod (36.0 cm = 0.36 m)
L is the total length of the rod (14.0 cm = 0.14 m)
By plugging in the given values into the formula, we can calculate the electric field at the given point.
E = (9 * 10^9 N m^2/C^2 * (-20.0 * 10^-6 C) * 0.36 m) / ((0.14 m)^2 * sqrt((0.14 m/2)^2 + (0.36 m)^2))
Simplifying the equation, we get:
E = -90 N/C
So, the magnitude of the electric field along the axis of the rod at a point 36.0 cm from its center is 90 N/C.
Since the charge on the rod is negative, the electric field will be directed away from the rod. Therefore, the direction of the electric field is away from the rod.