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, you can use the formula for the electric field created by a uniformly charged rod.
The formula for the electric field (E) created by a uniformly charged rod at a point on its axis is given by:
E = (k * Q) / (L * √(L^2 + R^2))
Where:
- E is the magnitude of the electric field
- k is Coulomb's constant (9.0 x 10^9 Nm^2/C^2)
- Q is the total charge on the rod
- L is the length of the rod
- R is the distance from the center of the rod to the point where you want to determine the electric field.
In this case, we have the following values:
- 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
Substituting these values into the formula, we can calculate the electric field:
E = (9.0 x 10^9 Nm^2/C^2 * (-20.0 x 10^-6 C)) / (14.0 x 10^-2 m * √((14.0 x 10^-2 m)^2 + (36.0 x 10^-2 m)^2))
Evaluating this expression will give you the magnitude of the electric field.
To determine the direction of the electric field, you need to consider the sign of the charge. In this case, the charge is negative, which means the electric field will point towards 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 the electric field due to a uniformly charged rod:
E = (k * λ) / r,
where:
E is the electric field,
k is the Coulomb's constant (9.0 x 10^9 N m²/C²),
λ is the linear charge density, and
r is the distance from the center of the rod.
First, let's calculate the linear charge density (λ):
λ = Q / L,
where:
Q is the total charge of the rod (-20.0 µC), and
L is the length of the rod (14.0 cm).
λ = (-20.0 x 10^-6 C) / (14.0 x 10^-2 m),
λ = -1.43 x 10^-3 C/m.
Now, substitute the values into the electric field formula:
E = (9.0 x 10^9 N m²/C²) * (-1.43 x 10^-3 C/m) / (36.0 x 10^-2 m).
E = -3.58 x 10^5 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 3.58 x 10^5 N/C. Since the formula for electric field is a vector quantity, we can say the direction is along the negative direction of the axis of the rod.