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
direction toward
casa
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 due to a uniformly charged rod is given by:
E = (k * Q) / r²
Where:
E is the electric field
k is the electrostatic constant (9.0 x 10^9 N m²/C²)
Q is the charge of the rod
r is the distance from the center of the rod to the point where we want to calculate the electric field
Given:
Q = -20.0 µC = -20.0 x 10^-6 C
r = 36.0 cm = 36.0 x 10^-2 m
Let's calculate the electric field:
E = (9.0 x 10^9 N m²/C² * (-20.0 x 10^-6 C)) / (36.0 x 10^-2 m)²
E = -180 x 10^3 N/C / (36.0 x 10^-2 m)²
E = -180 x 10^3 N/C / 1.296 x 10^-2 m²
E ≈ -138.9 x 10^3 N/C
The magnitude of the electric field is approximately 138.9 x 10^3 N/C.
Since the charge of the rod is negative (-20.0 µC) and the electric field is negative (-138.9 x 10^3 N/C), the direction of the electric field is toward the rod.
Therefore, the magnitude of the electric field is approximately 138.9 x 10^3 N/C, and it is directed toward the rod.
To determine the magnitude and direction of the electric field along the axis of the rod at a specific point, we can use the concept of electric field due to a uniformly charged rod.
The electric field at a distance x along the axis of a uniformly charged rod can be calculated using the formula:
E = (k * Q * x) / (L^2 * sqrt(L^2 + 4x^2))
Where:
E - Electric field magnitude
k - Coulomb's constant (k = 9 * 10^9 N*m^2/C^2)
Q - Total charge on the rod
x - Distance along the axis of the rod
L - Length of the rod
In this case, we are given:
Q = -20.0 µC (-20.0 * 10^-6 C)
L = 14.0 cm (converted to meters: 14.0 * 10^-2 m)
x = 36.0 cm (converted to meters: 36.0 * 10^-2 m)
Now let's substitute the values into the formula and calculate the electric field:
E = (9 * 10^9 N*m^2/C^2 * -20.0 * 10^-6 C * 36.0 * 10^-2 m) / ((14.0 * 10^-2 m)^2 * sqrt((14.0 * 10^-2 m)^2 + 4 * (36.0 * 10^-2 m)^2))
E = -1.371 N/C
The negative sign indicates that the electric field is directed away from the rod. Therefore, the magnitude of the electric field along the axis of the rod at a point 36.0 cm from its center is 1.371 N/C, and it is directed away from the rod. Therefore, the correct answer is "away from the rod."