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

Questions

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 and the principle of superposition.

1. First, let's calculate the electric field due to each half of the rod separately and then combine the contributions.

2. The electric field due to a point charge at a distance r along its axis is given by the formula:
E = k * (Q / r^2)
where E is the electric field, k is the electrostatic constant (9 x 10^9 Nm^2/C^2), Q is the charge, and r is the distance.

3. Considering one half of the rod, the charge Q will be -20.0 µC / 2 = -10.0 µC since the rod is uniformly charged.

4. The distance from the center of the rod to the point is 36.0 cm = 0.36 m.

5. Now, let's calculate the electric field due to one half of the rod at the given point:
E1 = k * (Q / r^2)
E1 = (9 x 10^9 Nm^2/C^2) * (-10.0 x 10^-6 C) / (0.36 m)^2

Calculate the value of E1.

6. Next, we need to consider the electric field due to the other half of the rod, which will have the same magnitude as E1 but in the opposite direction.

7. Therefore, the total electric field at the given point is the sum of E1 and the electric field due to the other half of the rod.

8. Finally, calculate the total electric field by combining the magnitudes and directions of the electric fields from steps 5 and 7.

After performing the calculations, you will find the magnitude and direction of the electric field along the axis of the rod at the given point.

To determine the magnitude and direction of the electric field along the axis of the rod at a specific point, we can use the formula for the electric field due to a uniformly charged rod:

E = k * (Q / r^2) * (sqrt(L^2 + r^2) - sqrt(L^2 - r^2))

Where:
- E is the electric field
- k is the Coulomb's constant (k = 9 x 10^9 N*m^2/C^2)
- Q is the total charge of the rod
- r is the distance from the center of the rod to the point where we want to determine the electric field
- L is the length of the rod

Let's plug in the given values into the formula:

E = (9 x 10^9 N*m^2/C^2) * (-20.0 x 10^-6 C) / (0.36^2) * (sqrt(0.14^2 + 0.36^2) - sqrt(0.14^2 - 0.36^2))

Simplifying the equation:

E = (-20.0 x 10^-6) * (9 x 10^9) * (sqrt(0.14^2 + 0.36^2) - sqrt(0.14^2 - 0.36^2)) / (0.36^2)

Calculating the value:

E ≈ -2877 N/C

The negative sign indicates that the electric field points in the opposite direction of conventional current flow, or in this case, from right to left along the axis of the rod. So the magnitude of the electric field is approximately 2877 N/C, and its direction is from right to left.

dude