Two 10-cm-diameter charged rings face each other, 15.0 cm apart. Both rings are charged to + 30.0 nC . What is the electric field strength at the center of the left ring?
To find the electric field strength at the center of the left ring, we can use the principle of superposition. According to this principle, the total electric field at a point due to multiple charges is the vector sum of the electric fields produced by each individual charge.
Here's how you can find the electric field at the center of the left ring:
1. Calculate the electric field due to the first ring:
- The electric field due to a uniformly charged ring at a point on its axis can be given by the formula:
E = (k * Q * x) / (2 * R^2 * sqrt(R^2 + x^2))
- Where E is the electric field, k is Coulomb's constant (9 x 10^9 N m^2/C^2), Q is the charge on the ring, x is the distance of the point from the center of the ring, and R is the radius of the ring.
- In this case, the radius of the ring is 10 cm which is equal to 0.1 m, and the charge on the ring is 30.0 nC which is equal to 30.0 x 10^-9 C.
- At the center of the left ring, the distance to the point on the axis of the ring is equal to half the distance between the two rings, which is 7.5 cm or 0.075 m.
- Plugging in the values into the formula, you can calculate the electric field due to the first ring at the center of the left ring.
2. Calculate the electric field due to the second ring:
- Since the second ring is identical to the first one and placed at the same distance from the center as the first ring, the electric field due to the second ring at the center of the left ring will be the same as the electric field due to the first ring.
3. Find the total electric field:
- The total electric field at the center of the left ring is the vector sum of the electric fields due to the first and second rings since the electric fields are in the same direction.
- Add the magnitudes of the electric fields due to the first and second rings together to get the final result.
Following these steps, you should be able to calculate the electric field strength at the center of the left ring.