Two 8 cm long thin glass rods uniformly charged to +10 nC are placed side by side, 4.0 cm apart. What are the electric field strengths E1 to E3 at distances 1.0 cm, 2.0 cm, and 3.0 cm to the right of the rod on the left along the line connecting the midpoints of the two rods?
To find the electric field strengths at different distances, we can use Coulomb's Law. Coulomb's Law states that the electric field produced by a charged particle is directly proportional to its charge and inversely proportional to the square of the distance from the particle.
First, let's find the electric field produced by one of the glass rods at a distance of 1.0 cm, 2.0 cm, and 3.0 cm to the right of the rod on the left.
1. Calculate the electric field at distance 1.0 cm:
- Electric field at a point due to a charged rod is given by the equation:
E = k * (Q / r^2)
where k is the electrostatic constant (k = 9 x 10^9 Nm^2/C^2), Q is the charge, and r is the distance.
- Substitute the given values:
E1 = (9 x 10^9 Nm^2/C^2) * (10 x 10^-9 C) / (0.01^2 m)
2. Calculate the electric field at distance 2.0 cm:
- Substitute the values into the equation:
E2 = (9 x 10^9 Nm^2/C^2) * (10 x 10^-9 C) / (0.02^2 m)
3. Calculate the electric field at distance 3.0 cm:
- Substitute the values into the equation:
E3 = (9 x 10^9 Nm^2/C^2) * (10 x 10^-9 C) / (0.03^2 m)
Now let's calculate the values:
E1 = (9 x 10^9 Nm^2/C^2) * (10 x 10^-9 C) / (0.01^2 m) = 900 N/C
E2 = (9 x 10^9 Nm^2/C^2) * (10 x 10^-9 C) / (0.02^2 m) = 225 N/C
E3 = (9 x 10^9 Nm^2/C^2) * (10 x 10^-9 C) / (0.03^2 m) = 100 N/C
Therefore, the electric field strength at distances 1.0 cm, 2.0 cm, and 3.0 cm to the right of the rod on the left along the line connecting the midpoints of the two rods are E1 = 900 N/C, E2 = 225 N/C, and E3 = 100 N/C, respectively.