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 the formula for the electric field due to a charged rod:
E = (k * Q) / (L * d)
where:
E is the electric field,
k is Coulomb's constant (9.0 x 10^9 N m^2/C^2),
Q is the total charge on the rod (-20.0 µC = -20.0 x 10^-6 C),
L is the length of the rod (14.0 cm = 0.14 m),
and d is the distance between the rod and the point where we want to calculate the electric field (36.0 cm = 0.36 m).
Using these values, we can calculate:
E = (9.0 x 10^9 N m^2/C^2 * -20.0 x 10^-6 C) / (0.14 m * 0.36 m)
E = -9.0 x 10^9 N m^2/C^2 * 20.0 x 10^-6 C / (0.14 m * 0.36 m)
E = -128 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 128 N/C. The negative sign indicates that the direction of the electric field is 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 equation for the electric field created by a uniformly charged rod:
E = k * (Q / r^2)
where E is the electric field, k is the Coulomb's constant (8.99 x 10^9 N·m^2/C^2), Q is the total charge of the rod, and r is the distance from the center of the rod.
Given:
- Length of the rod, l = 14.0 cm
- Total charge of the rod, Q = -20.0 µC
- Distance from the center of the rod, r = 36.0 cm
First, let's convert the length and distance from centimeters to meters:
l = 14.0 cm = 0.14 m
r = 36.0 cm = 0.36 m
Now, we can plug the given values into the equation for the electric field:
E = (8.99 x 10^9 N·m^2/C^2) * (-20.0 x 10^-6 C) / (0.36 m)^2
Calculating this expression will give us the magnitude of the electric field. Let's do the math:
E = (8.99 x 10^9) * (-20.0 x 10^-6) / (0.36)^2
E = -44.75 x 10^3 / 0.1296
E = -346.1 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 346.1 N/C. The negative sign indicates that the direction of the electric field is towards the center of the rod.
Example 2.2: Electric Field on the Axis of a Rod (page 2-17)
http://web.mit.edu/viz/EM/visualizations/coursenotes/modules/guide02.pdf